{"id":262,"date":"2023-07-10T06:09:02","date_gmt":"2023-07-10T06:09:02","guid":{"rendered":"https:\/\/mathority.org\/id\/persamaan-garis-semua-rumus-contoh-latihan-yang-diselesaikan\/"},"modified":"2023-07-10T06:09:02","modified_gmt":"2023-07-10T06:09:02","slug":"persamaan-garis-semua-rumus-contoh-latihan-yang-diselesaikan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/persamaan-garis-semua-rumus-contoh-latihan-yang-diselesaikan\/","title":{"rendered":"Persamaan garis"},"content":{"rendered":"<p>Di sini Anda akan menemukan rumus semua jenis persamaan garis. Selain itu, Anda akan dapat melihat contoh cara menghitungnya dan, sebagai tambahan, berlatih dengan latihan persamaan garis yang telah diselesaikan. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcuales-son-todas-las-ecuaciones-de-la-recta\"><\/span> Apa saja persamaan garisnya?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ingatlah bahwa definisi matematis garis adalah sekumpulan titik berurutan yang direpresentasikan dalam arah yang sama tanpa kurva atau sudut.<\/p>\n<p> Jadi, untuk menyatakan secara analitis setiap garis lurus pada bidang (dalam R2) kita menggunakan persamaan garis lurus, dan untuk menemukannya Anda hanya memerlukan sebuah titik yang termasuk dalam garis lurus tersebut dan vektor arah dari garis lurus tersebut. Hanya dengan dua elemen geometri ini, Anda dapat menemukan semua persamaan garis yang berbeda, yaitu sebagai berikut:<\/p>\n<p> <strong>Persamaan garis adalah persamaan vektor, persamaan parametrik, persamaan kontinu, persamaan implisit (atau umum), persamaan eksplisit, persamaan titik-kemiringan, dan persamaan kanonik (atau segmental).<\/strong><\/p>\n<p> Semua jenis persamaan garis memiliki tujuan yang sama: merepresentasikan garis secara matematis. Tetapi setiap persamaan garis mempunyai sifat-sifatnya masing-masing dan oleh karena itu, tergantung pada masalahnya, lebih baik menggunakan salah satu persamaan tersebut. <\/p>\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equations-de-la-droite-1.webp\" alt=\"persamaan garis pdf\" width=\"287\" height=\"273\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Setelah kita melihat konsep persamaan garis, sekarang kita beralih ke analisis karakteristik masing-masing jenis persamaan garis secara khusus. Di bawah ini Anda memiliki penjelasan rinci tentang berbagai jenis persamaan pada garis, tetapi jika mau, Anda dapat langsung menuju ke akhir <a href=\"https:\/\/mathority.org\/id\/persamaan-garis-semua-rumus-contoh-latihan-yang-diselesaikan\/\">tabel ringkasan dengan rumus semua persamaan pada garis<\/a> . <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-vectorial-de-la-recta\"><\/span> Persamaan vektor garis<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Ya<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah vektor arah garis dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> suatu titik yang berada di sebelah kanan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8a5a9724c5deabef496a75b00995419d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (\\text{v}_1,\\text{v}_2) \\qquad P(P}_1,P_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <strong>Rumus persamaan vektor garis<\/strong> adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6e64023d7dbfb100dc641c09e202e2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      (x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2) \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Emas:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah koordinat kartesius dari setiap titik pada garis.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d38a31ec1eb0a45c9ee8e1b143e3b4b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c78cc5579163a0956b9462599d75b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah koordinat suatu titik yang diketahui membentuk bagian garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6773414e1c04325d3dcb0a9f1e232f9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(P}_1,P_2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16a61eafb9e0a7b88b98a7fffd74c09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43a68c72834dd1643b28f72554b27956_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah komponen vektor arah garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-52295cf8445bb05e7ea88d57dca521e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(\\text{v}_1,\\text{v}_2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah skalar (bilangan real) yang nilainya bergantung pada setiap titik pada garis.<\/li>\n<\/ul>\n<p> Ini adalah persamaan vektor garis pada bidang, yaitu ketika bekerja dengan titik dan vektor 2 koordinat (dalam R2). Namun, jika kita melakukan perhitungan dalam ruang (dalam R3), kita harus menambahkan komponen tambahan pada persamaan garis: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ef53596406b2fe36258a0421c91336b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_1,P_2,P_3)+t\\cdot (\\text{v}_1,\\text{v}_2,\\text{v}_3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"288\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuaciones-parametricas-de-la-recta\"><\/span> Persamaan parametrik garis<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Persamaan parametrik suatu garis dapat diperoleh dari persamaan vektornya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Kita kalikan dulu parameternya<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> dengan vektor arah ke kanan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fdb6864861b77af0532f9a000fe566d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+ (t\\cdot\\text{v}_1,t\\cdot\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"239\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Selanjutnya kita tambahkan koordinat X dan Y:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bbd7cd2cffb8ff3378d0a03949644e0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1+t\\cdot\\text{v}_1,P_2+t\\cdot\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"239\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dan, terakhir, dengan membersihkan setiap variabel secara terpisah, kita memperoleh persamaan parametrik garis:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-46f6cdd4b1d1a92d038d140904abd119_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\displaystyle \\begin{cases} x=P_1+t\\cdot\\text{v}_1 \\\\[1.7ex] y=P_2+t\\cdot\\text{v}_2 \\end{cases} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Emas:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah koordinat Cartesius dari setiap titik pada garis.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d38a31ec1eb0a45c9ee8e1b143e3b4b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c78cc5579163a0956b9462599d75b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah koordinat suatu titik yang diketahui membentuk bagian garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6773414e1c04325d3dcb0a9f1e232f9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(P}_1,P_2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16a61eafb9e0a7b88b98a7fffd74c09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43a68c72834dd1643b28f72554b27956_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah komponen vektor arah garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-52295cf8445bb05e7ea88d57dca521e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(\\text{v}_1,\\text{v}_2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah skalar (bilangan real) yang nilainya bergantung pada setiap titik pada garis.<\/li>\n<\/ul>\n<p> Seperti sebelumnya, berikut adalah persamaan parametrik garis pada bidang (dalam R2), namun untuk mencari persamaan parametrik garis dalam ruang (dalam R3) perlu ditambahkan satu persamaan lagi untuk variabel ketiga Z: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e31f05449ce57a8af9ae4dda38535013_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases} x=P_1+t\\cdot\\text{v}_1 \\\\[1.7ex] y=P_2+t\\cdot\\text{v}_2 \\\\[1.7ex] z=P_3+t\\cdot\\text{v}_3\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-continua-de-la-recta\"><\/span>Persamaan garis kontinu<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Persamaan kontinu suatu garis dapat disimpulkan dari persamaan parametriknya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-708dbb33878e2bab0dcc94c84f6ab670_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases} x=P_1+t\\cdot\\text{v}_1 \\\\[1.7ex] y=P_2+t\\cdot\\text{v}_2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Jika kita menghapus pengaturannya<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> dari setiap persamaan parametrik kita memperoleh ekspresi berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-50f7c5405a4fc4f6faa3b8f4b651fb97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t =\\cfrac{x-P_1}{\\text{v}_1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"83\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-de8a9e455480e01bf5166f9519430491_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t =\\cfrac{y-P_2}{\\text{v}_2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"83\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> E Dengan menyamakan kedua persamaan yang dihasilkan, kita memperoleh persamaan garis kontinu:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26c55cd229e56a297715f1c05891a523_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t= t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"36\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-913e6797e350e331ce17df6b5c074f91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x-P_1}{\\text{v}_1}=\\cfrac{y-P_2}{\\text{v}_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"127\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> Singkatnya, <strong>persamaan garis kontinu<\/strong> adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7063ed965532bc4df04315115aa10bdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\cfrac{x-P_1}{\\text{v}_1}=\\cfrac{y-P_2}{\\text{v}_2} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Emas:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah koordinat Cartesius dari setiap titik pada garis.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d38a31ec1eb0a45c9ee8e1b143e3b4b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c78cc5579163a0956b9462599d75b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah koordinat suatu titik yang diketahui membentuk bagian garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6773414e1c04325d3dcb0a9f1e232f9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(P}_1,P_2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16a61eafb9e0a7b88b98a7fffd74c09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43a68c72834dd1643b28f72554b27956_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah komponen vektor arah garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-52295cf8445bb05e7ea88d57dca521e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(\\text{v}_1,\\text{v}_2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p> Rumus ini untuk persamaan garis kontinu bila dikerjakan dalam 2 dimensi (dalam 2D). Namun jika kita melakukan operasi dalam 3 dimensi (3D), kita perlu menambahkan komponen tambahan pada persamaan garis: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a090d35f6f6edef6dfff9c124862a49a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x-P_1}{\\text{v}_1}=\\cfrac{y-P_2}{\\text{v}_2}= \\cfrac{z-P_3}{\\text{v}_3}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"202\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-implicita-o-general-de-la-recta\"><\/span> Persamaan garis implisit atau umum<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Ya<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah vektor arah garis dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> suatu titik yang berada di sebelah kanan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8a5a9724c5deabef496a75b00995419d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (\\text{v}_1,\\text{v}_2) \\qquad P(P}_1,P_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Rumus <strong>persamaan garis implisit, umum atau kartesius<\/strong> adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acd74645ce35f9b771269d09bb1e0b9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      Ax+By+C=0 \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Emas:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah koordinat Cartesius dari setiap titik pada garis.<\/li>\n<li> koefisien\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah komponen kedua dari vektor arah garis:<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8aae57bb8c0ba7650d53c865bdf4855a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=\\text{v}_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -3px;\"><\/p>\n<\/li>\n<li> koefisien\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah komponen pertama dari tanda perubahan vektor arah:<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a42f7e7fc1557de4f36ee335a3ff6c64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B=-\\text{v}_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: -3px;\"><\/p>\n<\/li>\n<li> koefisien\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f34f74d98915e33f37a086f8cbfb996a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> dihitung dengan mengganti titik yang diketahui<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalam persamaan garis.<\/li>\n<\/ul>\n<p> rumusnya, persamaan implisit suatu garis juga dapat diperoleh dengan mengalikan pecahan persamaan kontinu tersebut. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-explicita-de-la-recta\"><\/span> Persamaan garis eksplisit<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Rumus <strong>persamaan garis eksplisit<\/strong> adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-70bd24576c0a37b64c5731799e67083e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      y=mx+n \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Emas:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah kemiringan garis.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> perpotongannya dengan sumbu Y, yaitu ketinggian perpotongannya dengan sumbu Y.<\/li>\n<\/ul>\n<p> Pada bagian di bawah ini Anda akan melihat bagaimana parameter ditentukan<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> dari garis lurus Namun, khususnya, cara lain untuk mencari persamaan eksplisit adalah dengan menggunakan persamaan implisit; untuk ini, hal yang tidak diketahui harus diselesaikan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> dari persamaan implisit.<\/p>\n<h4 class=\"wp-block-heading\"> Arti parameter m dan n<\/h4>\n<p> Seperti yang kita lihat pada definisi persamaan garis eksplisit, parameter<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah kemiringan garis dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> perpotongan y-nya. Tapi apa maksudnya? Mari kita lihat ini dari representasi grafis sebuah garis: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-explicite-d-une-ligne.webp\" alt=\"Berapakah persamaan eksplisit garis y=mx+b\" class=\"wp-image-1455\" width=\"339\" height=\"339\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Istilahnya mandiri<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-565fee0d356edf7fb1f49b6e7eec8e61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> <strong>adalah titik potong garis dengan sumbu komputer<\/strong> (sumbu OY). Misalnya pada grafik di atas<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> sama dengan 1 karena garis tersebut memotong sumbu y di y=1.<\/p>\n<p> Di sisi lain, istilahnya<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f26b1f086c6ad942d7c0dac86a8338fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> <strong>menunjukkan kemiringan garis<\/strong> , yaitu kemiringannya. Seperti yang Anda lihat pada grafik,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> sama dengan 2 karena garis naik 2 satuan vertikal untuk 1 satuan horizontal.<\/p>\n<p> Jelasnya, jika kemiringannya positif maka fungsinya bertambah (naik), sebaliknya jika kemiringannya negatif maka fungsinya menurun (turun).<\/p>\n<h5 class=\"wp-block-heading\"> Menghitung kemiringan suatu garis<\/h5>\n<p> Setelah kita mengetahui secara pasti kemiringan suatu garis, mari kita lihat cara menghitungnya. Jadi, ada 3 cara berbeda untuk menentukan kemiringan suatu garis secara numerik:<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">Diberikan dua titik berbeda pada garis tersebut\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-99906702500e51b12e2859cc804a7b57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(x_1,y_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-460a66d684215738da922dc45a35aed0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_2(x_2,y_2),\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<p> Kemiringan garis sama dengan:<\/li>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ca826248e812d4f19056960777cb00f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\cfrac{\\Delta y}{\\Delta x} = \\cfrac{y_2-y_1}{x_2-x_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"150\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#000000;font-weight: normal;\">Ya\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-867fb10d1409b3d95ff447f6a095219d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> adalah vektor arah garis, kemiringannya adalah:<\/li>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60d899a76c2b7588e60dc3734a47019f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\cfrac{\\text{v}_2}{\\text{v}_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"59\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#000000;font-weight: normal;\">Ya\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f0b6b1a01f8fcc2f95be0364c090397_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p><\/span> adalah sudut yang dibentuk oleh garis dengan sumbu absis (sumbu X), kemiringan garis tersebut ekuivalen dengan garis singgung sudut tersebut: <\/li>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c76cc82b1d172b2b5af3b053752befac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\text{tg}(\\alpha )\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/ol>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-de-l-equation-explicite-d-une-ligne.webp\" alt=\"rumus persamaan garis eksplisit\" class=\"wp-image-1465\" width=\"288\" height=\"356\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-punto-pendiente-de-la-recta\"><\/span> Persamaan titik-kemiringan garis<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Rumus <strong>persamaan titik-kemiringan garis<\/strong> adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3d1f485a8e43f9f81d8711d2f17dac20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      y-P_2=m(x-P_1) \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Emas:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah kemiringan garis.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a4c0be0b31844a0cd94ce4d5ea2a7256_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1, P_2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"45\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah koordinat suatu titik pada garis <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a813701c043bb25e074ddaba52d46a0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(P_1,P_2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-canonica-o-segmentaria-de-la-recta\"><\/span> Persamaan garis kanonik atau segmental<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Meskipun varian persamaan garis ini kurang dikenal, persamaan garis kanonik dapat diperoleh dari titik potong garis dengan sumbu kartesius.<\/p>\n<p> Misalkan dua titik potong dengan sumbu suatu garis adalah:<\/p>\n<p class=\"has-text-align-center\"> Potong dengan sumbu X:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-73f7f9618f43f69c0d8a68ff9b47ffef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> Potong dengan sumbu Y:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aee2e1bda5b37d0b02db636b7d6a73e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <strong>Rumus persamaan garis kanonik<\/strong> adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f6882981d96c9f3eb383d6a005eca81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\cfrac{x}{a}+\\cfrac{y}{b} = 1  \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-canonique-segmentaire-ou-symetrique-d-une-ligne.webp\" alt=\"persamaan kalkulator garis\" class=\"wp-image-3261\" width=\"297\" height=\"298\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Dalam matematika, persamaan garis kanonik disebut juga persamaan segmental atau persamaan simetris.<\/p>\n<p> Di sisi lain, koefisien<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> Mereka juga dapat dicari dari persamaan garis umum dengan menggunakan rumus berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02f4d03229cc8bd79a81b676a8132f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"137\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ebb3b443a8362ad9f023f8a2df2f17b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a = -\\cfrac{C}{A} \\qquad \\qquad b = -\\cfrac{C}{B}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"196\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" id=\"tabla-resumen-formulas-de-todas-las-ecuaciones-de-la-recta\"><span class=\"ez-toc-section\" id=\"todas-las-ecuaciones-de-la-recta-formulas\"><\/span> Semua persamaan garis (rumus)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ringkasnya, berikut adalah tabel yang menunjukkan rumus semua persamaan garis: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/toutes-les-equations-des-formules-de-ligne.webp\" alt=\"\" class=\"wp-image-3276\" width=\"581\" height=\"451\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-las-ecuaciones-de-la-recta\"><\/span> Contoh penghitungan persamaan garis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sekarang kita telah melihat penjelasan keseluruhan tentang persamaan garis, mari kita lihat bagaimana suatu masalah umum persamaan garis diselesaikan:<\/p>\n<ul>\n<li> Temukan semua persamaan garis yang ditentukan oleh titik tersebut\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan vektornya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fe319cb0fecedf2052e6c1e4c856733_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4ffa6488af1fcaf91bd9e53fd9133451_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,-1) \\qquad \\qquad \\vv{\\text{v}}=(2,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Pertama-tama kita cari persamaan vektor garis dari rumusnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Cukup substitusikan koordinat titik dan vektor ke dalam rumus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-499cd8e60d74a468d0f312e9cd346a35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\bm{(x,y)=(3,-1)+t\\cdot (2,4)} \\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"534\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Kedua, kita menemukan persamaan parametrik garis melalui rumus yang sesuai:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2e6878c4d9b80337639f5fa7728a9f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} x=P_1+t\\cdot\\text{v}_1 \\\\[1.7ex] y=P_2+t\\cdot\\text{v}_2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b4690a2ab033a4016f2d16b9554ddea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\begin{cases} \\bm{x=3+2t} \\\\[1.7ex] \\bm{y=-1+4t} \\end{cases} \\quad \\vphantom{\\cfrac{\\cfrac{1}{2}}{\\cfrac{1}{2}}} }\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"467\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan kita juga menentukan persamaan garis kontinu dengan rumusnya : <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-913e6797e350e331ce17df6b5c074f91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x-P_1}{\\text{v}_1}=\\cfrac{y-P_2}{\\text{v}_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"127\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f2f5db81c1d59dde56d49b2fbb142f19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x-3}{2}=\\cfrac{y-(-1)}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"134\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f16821949f92a6284906d5a334bcc09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\cfrac{\\bm{x-3}}{\\bm{2}}\\bm{=}\\cfrac{\\bm{y+1}}{\\bm{4}}\\quad \\vphantom{\\Biggl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"434\" style=\"vertical-align: -28px;\"><\/p>\n<\/p>\n<p> Seperti yang Anda lihat, persamaan vektor, parametrik, dan kontinu mudah dihitung, Anda hanya perlu menggunakan rumusnya masing-masing.<\/p>\n<p> Sekarang mari kita beralih ke mencari persamaan garis umum (atau implisit). Untuk melakukan ini, kita menyilangkan dua pecahan dari persamaan kontinu: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a751eccdd3f40ccfa5794b381a5e89f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot (x-3)= 2 \\cdot (y+1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"174\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b811aa5db0504964c34ad20afa3d236b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x-12= 2y+2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"130\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b0a9ad69e0178c30b6e64e3c831d9c00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x-12-2y-2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"161\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3a3e29454fce63f0dfdfce4af94f1a12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad\\bm{4x-2y-14=0}\\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"466\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Sekarang kita dapat menentukan persamaan eksplisit penyelesaian garis untuk hal yang tidak diketahui<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> dari persamaan implisit: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c7353c2555925ed510b4981154f047e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x-2y-14=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"131\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-369e9cd3411a3f7feb8092114cd7ac46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2y=-4x+14\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"127\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-efc35d0e90899ca1c77e78a312bbf9f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-4x+14}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"116\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7dc1790cfc0976eb2b7affd9b541ea56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\bm{y=2x-7}\\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"418\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, kemiringan garis tersebut sama dengan 2 (suku yang menyertai variabel bebas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> ).<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1ee3bb14bbe97a1114d697f8b45a9f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan dengan ini kita dapat menghitung persamaan titik-kemiringan garis dengan rumusnya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f0c8bfe8364c4962a61ff66ab943aeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-P_2=m(x-P_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e3eec13b49d25de2c2f630cad81f4ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-(-1)=2(x-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3fea9b91fd8324deef9bae6501b30b6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad\\bm{y+1=2(x-3)}\\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"462\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Terakhir, untuk mencari persamaan segmental garis tersebut kita hitung titik potongnya dengan sumbu OX dan OY kemudian kita terapkan rumusnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9729cef93354933e4dcf55d23f640e45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=2x-7\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-53\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"> <span style=\"text-decoration: underline;\">Titik potong dengan sumbu absis (sumbu X)<\/span> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b58ae9c2cbc8637b603a8deb159c2ccb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0=2x-7\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-245f8be211088d9023ae23ea593765a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x=-7\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"78\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-68d1225afc848d605b122d88f9b9759d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-7}{-2} = \\cfrac{7}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"101\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fd7ca037d0505b02f143c65891bfd911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{7}{2}, 0\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"50\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"> <span style=\"text-decoration: underline;\">Titik potong dengan sumbu y (sumbu Y)<\/span> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3847d07e55ef57d0a7a39cc7b79f1c03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=2\\cdot 0-7\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"94\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c15f100d859ec9077a43994ca473b018_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=-7\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"56\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a5c4b18318739a0269d0ba45618ee45f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(0,-7\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c2f3b0119758235dab9c6000508936ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{a}+\\cfrac{y}{b} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"75\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0acb3effdbe516cb8f1dc3ede8eca716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad\\cfrac{\\bm{x}}{\\frac{\\bm{7}}{\\bm{2}}}+\\cfrac{\\bm{y}}{\\bm{-7}} \\bm{= 1} \\quad \\vphantom{\\Biggl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"422\" style=\"vertical-align: -28px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-de-la-recta-que-pasa-por-dos-puntos\"><\/span> persamaan garis lurus yang melalui dua titik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Masalah umum lainnya dalam persamaan garis adalah mencari persamaan garis yang ditentukan oleh dua titik tertentu. Meskipun kita dapat menghitung vektor arah garis dengan 2 titik dan kemudian persamaannya, di bawah ini kami berikan rumus yang dapat digunakan untuk mencari persamaan garis tersebut secara langsung dan mudah.<\/p>\n<p> Perhatikan dua titik yang terletak pada sebuah garis:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37c795a7dbd872ca4e96199d5335efb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(x_1,y_1) \\qquad \\qquad P_2(x_2,y_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"220\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <strong>Rumus mencari persamaan garis dari 2 titiknya<\/strong> adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a249bd55d016ac1e7f34f42de22d6e99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      y-y_1= \\cfrac{y_2-y_1}{x_2-x_1} (x-x_1) \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Rumus ini memungkinkan kita menghitung secara langsung persamaan titik-kemiringan garis ketika kita diberikan 2 titik yang dilalui garis tersebut. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-las-ecuaciones-de-la-recta\"><\/span> Menyelesaikan masalah persamaan garis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Temukan persamaan vektor, persamaan parametrik, dan persamaan kontinu garis yang dibatasi oleh titik<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan vektor pengarahnya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fe319cb0fecedf2052e6c1e4c856733_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> Jadilah keduanya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dcc97a260264762a15a9baa7cf40f61b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,3) \\qquad \\qquad \\vv{\\text{v}}=(-1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama, kita menghitung persamaan vektor garis dari rumusnya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76d743d0188e28e2dbb0ad828a671b2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\bm{(x,y)=(0,3)+t\\cdot (-1,5)} \\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"534\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami kemudian menemukan persamaan parametrik garis menggunakan rumus yang sesuai: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2e6878c4d9b80337639f5fa7728a9f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} x=P_1+t\\cdot\\text{v}_1 \\\\[1.7ex] y=P_2+t\\cdot\\text{v}_2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a734c32ae40ca816c19b895e54916eb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} x=0+t\\cdot (-1) \\\\[1.7ex] y=3+t\\cdot 5\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"132\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bff16cf5ab85c87d8a866a2d74ea2a31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\begin{cases} \\bm{x=-t} \\\\[1.7ex] \\bm{y=3+5t} \\end{cases} \\quad \\vphantom{\\cfrac{\\cfrac{1}{2}}{\\cfrac{1}{2}}} }\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"453\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir, kita menentukan persamaan garis kontinu dengan rumusnya masing-masing: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-913e6797e350e331ce17df6b5c074f91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x-P_1}{\\text{v}_1}=\\cfrac{y-P_2}{\\text{v}_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"127\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-30b363ea4f3d08cad83314f97a489b4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x-0}{-1}=\\cfrac{y-3}{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"106\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7bf9c947876ffb8003c437997c799f3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\cfrac{\\bm{x}}{\\bm{-1}}\\bm{=}\\cfrac{\\bm{y-3}}{\\bm{5}}\\quad \\vphantom{\\Biggl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"415\" style=\"vertical-align: -28px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 2<\/h3>\n<p> Temukan persamaan implisit, persamaan eksplisit, dan persamaan titik-kemiringan garis yang ditentukan oleh titik tersebut<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan vektor arahnya adalah <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fe319cb0fecedf2052e6c1e4c856733_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a31faba9bf39a58f03087eaea99c0c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-4,3) \\qquad \\qquad \\vv{\\text{v}}=(2,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Rumus persamaan garis implisit adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02f4d03229cc8bd79a81b676a8132f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"137\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kita harus mencari koefisien A, B dan C. Yang tidak diketahui A dan B diperoleh dari koordinat vektor arah garis, karena persamaan berikut selalu dibuktikan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-caffe051bad6b2835981c69786d9c98f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (-B,A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, koefisien A adalah koordinat kedua vektor, dan koefisien B adalah koordinat pertama vektor yang diubah tandanya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9357fbcba6acde824f0fa1cc3e389a0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{c}\\vv{\\text{v}}= (-B,A) \\\\[2ex] \\vv{\\text{v}}= (2,6) \\end{array} \\right\\}\\longrightarrow \\begin{array}{l}A=6 \\\\[2ex] B=-2 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"226\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kita hanya perlu mencari koefisien C. Untuk melakukannya, kita harus mensubstitusikan titik yang kita ketahui termasuk dalam garis ke dalam persamaannya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a2db3b6a5db31cf3a61fcd309886826b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e82cb96c9d0a667fafc20ad216f728f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x-2y+C=0 \\ \\xrightarrow{x=-4 \\ ; \\ y=3} \\ 6\\cdot (-4)-2\\cdot 3+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"414\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06deb5d0e5a9ede569d5df8ebb81efac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-24-6+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"129\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c9f169aa941fe39d794dc14e328e6dcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-30+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"99\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-98e55b016b593186a4639d6755ce98be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C=30\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi persamaan garis implisit, umum atau kartesius adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df38e3e4991749df96b24d202e033f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad\\bm{6x-2y+30=0}\\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"466\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita dapat menentukan persamaan eksplisit penyelesaian garis untuk hal yang tidak diketahui<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> dari persamaan implisit: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6418dd689e7fe9e034c7bc979d6b3401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x-2y+30=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"131\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7bea9f5614281ca073dd0a12624dd8aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2y=-6x-30\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"127\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c61c7e6c7767bff1a07380b2aab05ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-6x-30}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"116\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7286e57d0abbd99815b3324e8194227c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\bm{y=3x+15}\\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"427\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kemiringan garisnya sama dengan 3 (suku sebelum variabel bebas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> ).<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-260107cba86a7b21e919180b1130050e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan dari nilai kemiringan garis tersebut kita dapat menghitung persamaan titik-kemiringan garis dengan rumusnya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f0c8bfe8364c4962a61ff66ab943aeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-P_2=m(x-P_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a35b2e6a22317e902b5cce4815ccd6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-3=3(x-(-4))\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-671def0bdf4e7cf62d2019cc5187a130_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad\\bm{y-3=3(x+4)}\\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"462\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 3<\/h3>\n<p> Tentukan 3 titik pada garis berikut, yang dinyatakan sebagai persamaan implisit atau umum: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-92f98258fe0de7bfdabef5dfa0b9678c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x+2y-8 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"122\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk menghitung suatu titik pada suatu garis, kita hanya perlu memberikan nilai pada salah satu variabel dan kemudian mencari nilai variabel lainnya pada titik tersebut.<\/p>\n<p class=\"has-text-align-left\"> Kami menghitung poin pertama dengan melakukan <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d762821a7c6da83f02380639f43ef8fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-21bfe654b6dd49f110abf58c6d3df214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot 0+2y-8 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"134\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fe00aaf21ee98c3036532591e2796987_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2y = 8\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cfff981f9d77c69e6b8339ecd141562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = \\cfrac{8}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"44\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-07c6b260c2e43f4545a7c1974de73cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03dff5e2c9b5389babf595bd961ba962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{P_1(0,4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami kemudian menemukan titik kedua yang memberikan nilai lain pada variabel tersebut<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-038741496726a75b03e91a2e030b0287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> Misalnya <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-adfd4b59a1c96b58188448b5fe50dec7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=1:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c99451893ed7c2a58fb423eeddcf5258_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot 1+2y-8 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"134\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4419d32ace4c25320f6875b7acd275f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2y = 8-4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b72eeccbfe9aa758d0cbda671640ad6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2y = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f9787827f5407a73e53398776daff63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = \\cfrac{4}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"44\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e47e82982611531964ade31826b9e254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b797693671aff6ba5e46c9808a3f20d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{P_2(1,2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir, kami menghitung poin ketiga dengan menyelesaikannya <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6aff213e5b8cce8e689840fc8f6b8413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41842e99d77e585e9c7a5417f41a3167_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot 2+2y-8 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"134\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-376f7dee73fe357a8c79a157c8b4a966_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2y = 8-8\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce9418065ff9df3f3d58e578cb45a9b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2y = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fff4ce6b62556e0291e3d191a0d05ee9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = \\cfrac{0}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"44\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d0d3e85f938e2ecfcc840836d5698d72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-930774e05056e449ca78c16287f4481c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{P_3(2,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 4<\/h3>\n<p> Temukan semua persamaan garis yang ditentukan oleh titik<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan vektornya <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7fe319cb0fecedf2052e6c1e4c856733_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e319f5d0c3f211308f1489efbc6665d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,4) \\qquad \\qquad \\vv{\\text{v}}=(-3,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"223\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama-tama kita cari persamaan vektor garis dari rumusnya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49afd56a168dbacfe6fa06f284c36b95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\bm{(x,y)=(-1,4)+t\\cdot (-3,6)} \\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"547\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kedua, kita menemukan persamaan parametrik garis melalui rumus yang sesuai: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2e6878c4d9b80337639f5fa7728a9f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} x=P_1+t\\cdot\\text{v}_1 \\\\[1.7ex] y=P_2+t\\cdot\\text{v}_2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f3bf46da9a68147118874a619f918077_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\begin{cases} \\bm{x=-1-3t} \\\\[1.7ex] \\bm{y=4+6t} \\end{cases} \\quad \\vphantom{\\cfrac{\\cfrac{1}{2}}{\\cfrac{1}{2}}} }\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"468\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kita juga menentukan persamaan garis kontinu dengan menggunakan rumusnya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-913e6797e350e331ce17df6b5c074f91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x-P_1}{\\text{v}_1}=\\cfrac{y-P_2}{\\text{v}_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"127\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2712f4cc5c10283e89aab8c241bd0c6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x-(-1)}{-3}=\\cfrac{y-4}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"134\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-507d9c42afbe40a47426d930cd655acd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\cfrac{\\bm{x+1}}{\\bm{-3}}\\bm{=}\\cfrac{\\bm{y-4}}{\\bm{6}}\\quad \\vphantom{\\Biggl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"434\" style=\"vertical-align: -28px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang mari kita beralih ke mencari persamaan garis implisit atau umum. Untuk melakukan ini, kita menyilangkan dua pecahan dari persamaan kontinu: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e622246f6aee3aeeae4e46c2ab273448_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6\\cdot (x+1)= -3 \\cdot (y-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"188\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-233758c9cfa6e67037f0d9ac3491646b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x+6= -3y+12\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"144\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dce0a8f03df8900f43824c6dfe4965db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x+6+3y-12=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"161\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca892beb6a3dad6875963c37005a06ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad\\bm{6x+3y-6=0}\\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"457\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita dapat menentukan persamaan eksplisit penyelesaian garis untuk hal yang tidak diketahui<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> dari persamaan implisit: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db879a59b656865b385242dd4c936671_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x+3y-6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"122\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa0f4f461dead11823094f6c10e35131_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3y=-6x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"105\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce147ff77e418ccac9df420b80b7955f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-6x+6}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"107\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b069b281c719aacd05068d3e41d953e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad \\bm{y=-2x+2}\\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"432\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kemiringan garis tersebut setara dengan -2 (suku yang menyertai variabel bebas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> ).<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cb69f8df8ea8c5935576ece37a640c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan dengan ini kita dapat menghitung persamaan titik-kemiringan garis dengan rumusnya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f0c8bfe8364c4962a61ff66ab943aeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-P_2=m(x-P_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f6be33c2f75c28cefd5edacf7415db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-4=-2(x-(-1))\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d31a0383074e6488a39acdf48b73cc64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad\\bm{y-4=-2(x+1)}\\quad \\vphantom{\\Bigl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"476\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Terakhir, untuk mencari persamaan segmen garis, kita hitung titik potong garis dengan sumbu OX dan OY kemudian kita gunakan rumusnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9ee9a398efc0528db8f6e51a774b2116_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=-2x+2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-56\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"> <span style=\"text-decoration: underline;\">Titik potong dengan sumbu absis (sumbu X)<\/span> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b3265e1ea6c0695580197ddb6f267c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0=-2x+2\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"95\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78019a5b7c3b3aed3f574c422cf48ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e05ddb74466e215ecc9c0b5dbe90e54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{2}{2} =1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad6e487184338b18ddb30720fb02a024_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(1, 0\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"> <span style=\"text-decoration: underline;\">Titik potong dengan sumbu y (sumbu Y)<\/span> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bbbba3968c6e6c8f20894507d3feed33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=-2\\cdot 0+2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"107\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-552d8ed773e160e229551b39aff39445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5350b2cb3b61a50c3ecb754aa4c44518_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(0,2\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c2f3b0119758235dab9c6000508936ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x}{a}+\\cfrac{y}{b} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"75\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0a9eb3e730af50fc6c543600ca010ce7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{exemple}{HTML}{2196F3} \\color{exemple} \\boxed{ \\color{black} \\quad\\cfrac{\\bm{x}}{\\bm{1}}+\\cfrac{\\bm{y}}{\\bm{2}} \\bm{= 1} \\quad \\vphantom{\\Biggl(}}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"408\" style=\"vertical-align: -28px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 5<\/h3>\n<p> Tentukan persamaan garis yang melalui dua titik berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40e2b3beb2ff2f058df5534f1bd6b925_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1 (4,-1) \\qquad \\qquad P_2(5,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"201\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Karena kita sudah mengetahui dua titik pada garis, maka kita langsung menerapkan rumus persamaan garis pada 2 titik tertentu:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f97d63f216910e7979937859fb90a10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_1= \\cfrac{y_2-y_1}{x_2-x_1} (x-x_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"193\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita substitusikan koordinat Cartesian titik-titik tersebut ke dalam rumus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c75c3e6820d69b59b21ff79e2aee3055_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-(-1)= \\cfrac{2-(-1)}{5-4} (x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"214\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir, kita menghitung kemiringan garis: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3646c71be87d906417e00a512450ca9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y+1= \\cfrac{3}{1} (x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"128\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a70434a562eb7d94f6ff02d23de896a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y+1= 3(x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Maka persamaan garis yang melalui kedua titik tersebut adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0e7c7f608e0e1ba52d453cad7a29e99d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y+1= 3(x-4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di sini Anda akan menemukan rumus semua jenis persamaan garis. Selain itu, Anda akan dapat melihat contoh cara menghitungnya dan, sebagai tambahan, berlatih dengan latihan persamaan garis yang telah diselesaikan. Apa saja persamaan garisnya? Ingatlah bahwa definisi matematis garis adalah sekumpulan titik berurutan yang direpresentasikan dalam arah yang sama tanpa kurva atau sudut. Jadi, untuk &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/persamaan-garis-semua-rumus-contoh-latihan-yang-diselesaikan\/\"> <span class=\"screen-reader-text\">Persamaan garis<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[48],"tags":[],"class_list":["post-262","post","type-post","status-publish","format-standard","hentry","category-polinomial"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Persamaan garis -<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/persamaan-garis-semua-rumus-contoh-latihan-yang-diselesaikan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Persamaan garis -\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan rumus semua jenis persamaan garis. Selain itu, Anda akan dapat melihat contoh cara menghitungnya dan, sebagai tambahan, berlatih dengan latihan persamaan garis yang telah diselesaikan. Apa saja persamaan garisnya? Ingatlah bahwa definisi matematis garis adalah sekumpulan titik berurutan yang direpresentasikan dalam arah yang sama tanpa kurva atau sudut. 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