{"id":227,"date":"2023-07-10T22:50:09","date_gmt":"2023-07-10T22:50:09","guid":{"rendered":"https:\/\/mathority.org\/id\/persamaan-titik-kemiringan-rumus-garis\/"},"modified":"2023-07-10T22:50:09","modified_gmt":"2023-07-10T22:50:09","slug":"persamaan-titik-kemiringan-rumus-garis","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/persamaan-titik-kemiringan-rumus-garis\/","title":{"rendered":"Titik persamaan \u2013 kemiringan garis"},"content":{"rendered":"<p>Di halaman ini, Anda akan menemukan rumus persamaan titik-kemiringan garis dan juga berbagai cara untuk menghitungnya. Selain itu, Anda akan dapat melihat beberapa contoh dan latihan dengan latihan yang diselesaikan langkah demi langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-ecuacion-punto-pendiente-de-la-recta\"><\/span> Rumus persamaan titik-kemiringan garis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Persamaan titik-kemiringan suatu garis adalah cara untuk menyatakan suatu garis secara matematis. Secara khusus, Anda hanya memerlukan kemiringan dan koordinat suatu titik pada garis untuk mencari persamaan titik-kemiringan suatu garis. <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> <strong>Rumus persamaan titik-kemiringan garis<\/strong> adalah sebagai 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-3441e1da8c7da5805b1133af77b14f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left;\"> Emas<\/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-0ef0a49d51c8cfd13e37df1b9090418b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_0, y_0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" 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-cf65a6c806bfd1aa7b641e609d9d4490_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x_0,y_0).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<p> Mari kita lihat <strong>bagaimana persamaan titik-kemiringan garis dihitung<\/strong> dengan menggunakan contoh:<\/p>\n<ul>\n<li> Tuliskan persamaan titik-kemiringan garis yang melalui titik tersebut\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2b2d9d38efcc8624f90eef92208f4e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<p> dan kemiringan m=3.<\/li>\n<\/ul>\n<p> Rumus persamaan titik-kemiringan garis adalah sebagai 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-3441e1da8c7da5805b1133af77b14f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam hal ini, pernyataan tersebut menyatakan bahwa kemiringan garis adalah m=3, sehingga persamaan garisnya adalah sebagai 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-4063450c1658fa496145cc18a36ff1bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=3(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Selanjutnya kita juga mengetahui bahwa garis melalui suatu 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-d2b2d9d38efcc8624f90eef92208f4e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<p> , oleh karena itu kita harus mensubstitusikan koordinat titik ini ke dalam persamaan:<\/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-d2b2d9d38efcc8624f90eef92208f4e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,-1)\" 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-5cd50c0d1730e27ca68d517d5c9adc76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=3(x-x_0) \\ \\xrightarrow{x_0=2 \\ ; \\ y_0=-1} \\ y-(-1)=3(x-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"419\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, persamaan titik-kemiringan garis 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-f6ea4a8565fcf350fb588d891a0cf9fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y+1=3(x-2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ingatlah bahwa selain persamaan titik-kemiringan, ada cara lain untuk menyatakan garis secara analitis: persamaan vektor, persamaan parametrik, persamaan kontinu, persamaan implisit (atau umum) dan persamaan garis eksplisit. Jika Anda lebih tertarik, Anda dapat memeriksa masing-masingnya di situs web kami. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-significa-la-pendiente-de-una-recta\"><\/span> Apa yang dimaksud dengan kemiringan suatu garis?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Seperti yang kita lihat pada definisi persamaan titik-kemiringan suatu garis, 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-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. Tapi sungguh\u2026 apa yang dimaksud dengan kemiringan suatu garis? Mari kita lihat ini dari representasi grafis sebuah garis: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/point-pente-equation.webp\" alt=\"Apa persamaan titik-kemiringan suatu garis?\" class=\"wp-image-1590\" width=\"317\" height=\"318\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> <strong>Kemiringan garis<\/strong> menunjukkan kecuramannya. Seperti yang Anda lihat dari garis grafik,<\/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> 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<h4 class=\"wp-block-heading\"> Cara menghitung kemiringan suatu garis<\/h4>\n<p> Selain itu, 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<div class=\"wp-block-image\">\n<figure class=\"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<\/div>\n<h4 class=\"wp-block-heading\"> Posisi relatif garis<\/h4>\n<p> Terakhir, kemiringan suatu garis juga digunakan untuk mengetahui hubungan beberapa garis. Karena dua garis <strong>sejajar<\/strong> mempunyai kemiringan yang sama, dan sebaliknya jika kemiringan suatu garis merupakan kebalikan negatif dari kemiringan garis yang lain, maka kedua garis tersebut <strong>tegak lurus<\/strong> . <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-161\">\n<div class=\"wp-block-column is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/lignes-paralleles-pente-dune-ligne.webp\" alt=\"garis sejajar dengan kemiringan yang sama\" class=\"wp-image-1550\" width=\"200\" height=\"201\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/lignes-perpendiculaires-pente-d-une-ligne.webp\" alt=\"\" class=\"wp-image-1551\" width=\"176\" height=\"260\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-la-ecuacion-punto-pendiente-de-la-recta-que-pasa-por-dos-puntos\"><\/span> Hitung persamaan titik-kemiringan garis yang melalui dua titik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Masalah yang sangat umum adalah menentukan persamaan titik-kemiringan dari dua titik yang termasuk dalam garis. Mari kita lihat bagaimana penyelesaiannya melalui sebuah contoh:<\/p>\n<ul>\n<li> Tentukan persamaan titik-kemiringan garis yang melalui dua titik berikut:<\/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-2eedda183214849aae2330021a513130_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(5,2) \\qquad P_2(3,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Untuk mencari persamaan titik-kemiringan suatu garis, kita perlu menentukan kemiringan garis tersebut. Jadi kita menghitung kemiringan garis menggunakan rumus titik dua:<\/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-355e91b09882111b8826f4bfe5d33698_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} = \\cfrac{6-2}{3-5} = \\cfrac{4}{-2}= -2\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"308\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> Jadi, persamaan titik-kemiringan garis tersebut adalah sebagai 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-3441e1da8c7da5805b1133af77b14f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" 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-bce5bf62dac701d1295a97495bafcac4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=-2(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, kita hanya perlu mensubstitusikan koordinat kartesius suatu titik pada garis tersebut ke dalam persamaan: <\/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-a03a686f78d6b7326bf8047caa76b8f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(5,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" 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-b0ef1c00c03b4a297e716ee315f99504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=-2(x-x_0) \\ \\xrightarrow{x_0=5 \\ ; \\ y_0=2} \\ y-2=-2(x-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"408\" 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-b11cf352f48c55c068de6d1d36f9f51f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y-2=-2(x-5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ada baiknya juga jika kita masukkan poin lain dari pernyataan tersebut ke dalam 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-e806d8b8c196642821eee52b8c199107_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(3,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" 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-988654f7c8782517dc9dabe3fca4a206_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-6=-2(x-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hallar-la-ecuacion-punto-pendiente-de-una-recta-a-partir-de-la-grafica\"><\/span> Temukan persamaan titik-kemiringan suatu garis dari grafik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Seperti yang kita lihat pada bagian di atas, ada beberapa cara untuk mencari persamaan titik-kemiringan suatu garis secara numerik. Namun, hal ini juga dapat ditemukan secara grafis. Mari kita lihat bagaimana hal ini dilakukan melalui sebuah contoh:<\/p>\n<ul>\n<li> Tentukan persamaan titik-kemiringan garis yang ditunjukkan pada grafik berikut: <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/point-pente-ligne-equation.webp\" alt=\"representasi grafis dari sebuah garis\" class=\"wp-image-1606\" width=\"314\" height=\"315\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Untuk menentukan persamaan titik-kemiringan garis yang ditarik, kita perlu mencari kemiringan dan titik pada garis tersebut.<\/p>\n<p> Dalam hal ini kemiringan garis sama dengan 3, karena garis naik 3 satuan vertikal untuk setiap satuan horizontal.<\/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-0082d45adbb746641eb28f250a819459_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> Selanjutnya kita memerlukan sebuah titik pada garis tersebut. Untuk melakukan ini, kita dapat memilih titik mana saja pada grafik yang dilalui garis, misalnya titik (1,1).<\/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-cc3450ac38bb3acc76eae31215c49b82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, sekarang kita dapat mencari persamaan titik-kemiringan garis dengan menerapkan 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-3441e1da8c7da5805b1133af77b14f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" 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-829ac7a79e34c45087cbfb472eacb856_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-1=3(x-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/determiner-lequation-point-pente-dune-ligne-graphiquement.webp\" alt=\"menentukan secara grafis kemiringan titik persamaan suatu garis\" class=\"wp-image-1607\" width=\"314\" height=\"315\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-ecuacion-punto-pendiente-de-la-recta\"><\/span> Menyelesaikan Masalah Persamaan Titik-Kemiringan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Tuliskan persamaan titik-kemiringan garis yang melalui 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-3e4a894322ba599f7554e658df9395ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<p> dan kemiringannya adalah <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e3505d96cc978cbd5e9fefda94605f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=-2.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"66\" style=\"vertical-align: 0px;\"><\/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 titik-kemiringan garis 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-3441e1da8c7da5805b1133af77b14f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dalam hal ini pernyataan tersebut menyatakan bahwa kemiringan garis adalah m=-2, sehingga persamaan garisnya adalah sebagai 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-bce5bf62dac701d1295a97495bafcac4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=-2(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Selanjutnya kita juga mengetahui dari pernyataan bahwa garis melalui suatu 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-3e4a894322ba599f7554e658df9395ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<p> , oleh karena itu cukup dengan mensubstitusikan koordinat titik tersebut ke dalam 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-3e4a894322ba599f7554e658df9395ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" 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-7e8f25bcb8e24f35f3ad9e64dbeab604_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y-4=-2(x-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" 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 2<\/h3>\n<p> Berapakah persamaan titik-kemiringan 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-1d87f163111868ca87a1e0d33e7373e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(1,6) \\qquad P_2(4,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" 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\"> Untuk mencari persamaan titik-kemiringan suatu garis, kita perlu menentukan kemiringan garis tersebut. Oleh karena itu kami menghitung 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-6587ef8551123fada18e66a19b120672_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} = \\cfrac{0-6}{4-1} = \\cfrac{-6}{3}= -2\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"316\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, persamaan titik-kemiringan garis tersebut adalah sebagai 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-3441e1da8c7da5805b1133af77b14f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" 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-bce5bf62dac701d1295a97495bafcac4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=-2(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kita hanya perlu mensubstitusikan koordinat suatu titik pada garis tersebut ke dalam persamaan: <\/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-bcbff883ed57a03d2b8c0ad3d99fbd8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(1,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" 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-65df3bba32eb4d9dc32e16c8c26fd81f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y-6=-2(x-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Benar juga jika poin lain dari pernyataan tersebut dimasukkan ke dalam persamaan: <\/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-e45755fe2812135fe1f4e39b3157fcf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=-2(x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" 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 3<\/h3>\n<p> Tentukan persamaan titik-kemiringan 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-fd4450de7b302ee03cef55687c1e7b01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(1,-2) \\qquad P_2(2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" 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\"> Untuk mencari persamaan titik-kemiringan suatu garis, Anda harus menghitung kemiringannya terlebih dahulu:<\/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-194cde1d2e3ba81c4bfce5bf0244c51a_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} = \\cfrac{3-(-2)}{2-1} = \\cfrac{3+2}{1}=\\cfrac{5}{1}= 5\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"373\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, persamaan titik-kemiringan garis tersebut adalah sebagai 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-3441e1da8c7da5805b1133af77b14f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" 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-7d740b976c2c72700bfcd9562e1d6236_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=5(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kita hanya perlu mensubstitusikan koordinat suatu titik pada garis tersebut ke dalam persamaan: <\/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-bd29b3293380effcfb027a6b7aec2252_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(1,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" 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-ba331d69618f15f523d0bef9b28673f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-(-2)=5(x-1)\" 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-0b7256b1d7a60559de4cbad1ffe360a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y+2=5(x-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Benar juga jika titik lain dalam pernyataan tersebut dimasukkan ke dalam 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-66fd02f8e38dc1b0a598a1a384e697c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-3=5(x-2)\" 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<h3 class=\"wp-block-heading\">Latihan 4<\/h3>\n<p> Hitung persamaan titik-kemiringan garis yang membentuk sudut 45\u00ba terhadap sumbu X dan melalui titik asal koordinat. <\/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\"> Jika garis membentuk sudut 45 derajat terhadap sumbu OX, kemiringannya 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-51d113bc9a4b67f4c35c31f08baa7ad9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\text{tg}(45\u00ba) = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" 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-7831f83b7ed770006cac5c20921bfa0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=1(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" 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-1d02fbbf78fbaf1ec868c2555515cad0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=x-x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"120\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan setelah kita mengetahui kemiringan garis, kita dapat mencari persamaan titik-kemiringan dengan mensubstitusikan sebuah titik pada garis ke dalam persamaan tersebut. Selain itu, pernyataan tersebut menyatakan bahwa garis melalui titik asal koordinat, yang berarti melalui titik (0,0). Belum: <\/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-048c1ceefde62a60b4cf2420a67d7f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" 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-f032721e5e51bcb17f57204a1991d5c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=x-x_0 \\ \\xrightarrow{x=0 \\ ; \\ y=0} \\ y-0=x-0\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"323\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, persamaan titik-kemiringan garis 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-4909df7491ef54f0df1e922bc29417f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=x}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: -4px;\"><\/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> Temukan persamaan kemiringan titik garis yang sejajar dengan garis 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-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan apa yang terjadi di titik tersebut<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37ecf61896ad8378d5128916dfa0db58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,-3).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<p> menjadi lurus <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5986f031932e6b3512dc564514c34b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" 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-13e021539041421cca99c04a0add9516_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\; y-1=2(x+5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" 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\"> 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-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> sama dengan 2 (angka sebelum tanda kurung), dan agar dua garis sejajar harus mempunyai kemiringan yang sama, oleh karena itu: <\/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-f3439899d4781058b8eb19021ac25e27_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 class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a8579f7a4e6d6535f68742555a229e8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=2(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan setelah kita mengetahui kemiringan garis tersebut, kita cukup mengganti koordinat suatu titik yang termasuk dalam garis 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-398c2be999567c477ccd7a55d5c66ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" 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-3ae615335baed1209de396f5a98fe6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-(-1)=2(x-(-3))\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"182\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, persamaan titik-kemiringan garis 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-45304f06d37b44e4b468dcea500c1689_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y+1=2(x+3)}\" 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<h3 class=\"wp-block-heading\">Latihan 6<\/h3>\n<p> Tentukan persamaan titik-kemiringan setiap garis yang ditunjukkan pada grafik berikut: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-dequation-de-la-ligne-explicite.webp\" alt=\"persamaan eksplisit latihan garis diselesaikan langkah demi langkah\" class=\"wp-image-1500\" width=\"377\" height=\"405\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\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\"> <strong>biru benar<\/strong><\/p>\n<p class=\"has-text-align-left\"> Garis biru bertambah satu Y untuk setiap X, sehingga kemiringannya sama dengan 1. Sebaliknya melalui titik (2,4), maka:<\/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-2da731e16044d6c6ac573d0f5ecdc8b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-4 =x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"103\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>hijau kanan<\/strong><\/p>\n<p class=\"has-text-align-left\"> Garis hijau bertambah tiga Y untuk setiap X, jadi kemiringannya adalah 3. Selain itu, salah satu titiknya adalah (2,2), jadi:<\/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-cda4faf329c19618c240327d8a427333_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-2 =3(x-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>garis merah<\/strong><\/p>\n<p class=\"has-text-align-left\"> Garis merah berkurang dua Y untuk setiap X, sehingga kemiringannya adalah -2. Dan titik (0,-2) termasuk dalam garis ini, oleh karena itu: <\/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-de1091d5afd35c2063ab769ade6bf7ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =-2(x+2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" 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 halaman ini, Anda akan menemukan rumus persamaan titik-kemiringan garis dan juga berbagai cara untuk menghitungnya. Selain itu, Anda akan dapat melihat beberapa contoh dan latihan dengan latihan yang diselesaikan langkah demi langkah. Rumus persamaan titik-kemiringan garis Persamaan titik-kemiringan suatu garis adalah cara untuk menyatakan suatu garis secara matematis. Secara khusus, Anda hanya memerlukan kemiringan &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/persamaan-titik-kemiringan-rumus-garis\/\"> <span class=\"screen-reader-text\">Titik persamaan \u2013 kemiringan 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":[47],"tags":[],"class_list":["post-227","post","type-post","status-publish","format-standard","hentry","category-titik-garis-dan-bidang"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Persamaan titik \u2013 kemiringan garis \u2013 Mathority<\/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-titik-kemiringan-rumus-garis\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Persamaan titik \u2013 kemiringan garis \u2013 Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini, Anda akan menemukan rumus persamaan titik-kemiringan garis dan juga berbagai cara untuk menghitungnya. 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