{"id":226,"date":"2023-07-10T23:13:43","date_gmt":"2023-07-10T23:13:43","guid":{"rendered":"https:\/\/mathority.org\/id\/kemiringan-rumus-garis\/"},"modified":"2023-07-10T23:13:43","modified_gmt":"2023-07-10T23:13:43","slug":"kemiringan-rumus-garis","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/kemiringan-rumus-garis\/","title":{"rendered":"Kemiringan suatu garis (rumus)"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan paling detail tentang kemiringan suatu garis: apa rumusnya, contoh perhitungannya, apa yang dimaksud dengan konsep kemiringan suatu garis,\u2026 Anda juga dapat melihat cara mudah mengidentifikasi kemiringan suatu garis. garis dari persamaannya dan, sebagai tambahan, Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-pendiente-de-una-recta\"><\/span> Rumus kemiringan suatu garis <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\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>Kemiringan suatu garis<\/strong> sama dengan perpindahan vertikal antara dua titik dibagi dengan perpindahan horizontal antara dua titik yang sama.<\/p>\n<p style=\"text-align:left\"> Artinya, diberikan dua titik 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-64af51bbaed8952d251997515c64b85c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(x_1,y_1) \\qquad P_2(x_2,y_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Rumus kemiringan suatu 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-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<\/div>\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\/pente-dune-ligne-1.webp\" alt=\"berapa kemiringan suatu garis\" class=\"wp-image-1523\" width=\"328\" height=\"312\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-la-pendiente-de-una-recta-a-partir-de-dos-puntos\"><\/span> Contoh menghitung kemiringan suatu garis dari dua titik <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p> Selanjutnya kita akan melihat contoh cara menghitung kemiringan suatu garis dengan rumus:<\/p>\n<ul>\n<li> Hitunglah 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-5625033af5d12379bbc5e375fd06888d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(3,1) \\qquad P_2(5,7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Untuk mencari kemiringan garis ini, cukup 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-a5b9ed9145447559a6eb62e27c584432_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{7-1}{5-3}=\\cfrac{6}{2} = \\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"281\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> Oleh karena itu kemiringan garisnya sama dengan 3. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hallar-la-pendiente-de-una-recta-a-partir-de-su-ecuacion\"><\/span> Mencari kemiringan suatu garis dari persamaannya <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p> Pada bagian di atas, kita baru saja melihat cara menentukan kemiringan suatu garis secara numerik. Namun tidak selalu perlu dilakukan perhitungan, tetapi nilainya juga dapat diketahui dari persamaan suatu garis. Setiap jenis persamaan berbeda, jadi kami akan menganalisis setiap kasus secara terpisah. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pendiente-dada-la-ecuacion-explicita-de-la-recta\"><\/span> Kemiringan diberikan persamaan garis yang eksplisit<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Persamaan garis eksplisit mengikuti 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-9f20f0b48ca24d4d8e36d110a7a9fab0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =\\color{blue}\\bm{m}\\color{black}x+n\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"163\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Lalu 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> sesuai dengan kemiringan garis. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pendiente-dada-la-ecuacion-punto-pendiente-de-la-recta\"><\/span> Kemiringan diberikan persamaan titik-kemiringan garis<span class=\"ez-toc-section-end\"><\/span><\/h3>\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-470b8b3f0e00bf809f6089864fe6dd44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y -y_0=\\color{blue}\\bm{m}\\color{black}(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Seperti sebelumnya, 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-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> sesuai dengan kemiringan garis. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pendiente-dada-la-ecuacion-implicita-de-la-recta\"><\/span> Kemiringan diberikan persamaan garis implisit<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Diketahui persamaan garis implisit (disebut juga persamaan umum atau persamaan Cartesius):<\/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> Kemiringan garis dapat dicari 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-94f59cc7d3c1b4ece0a70a3587fa0a77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=-\\cfrac{A}{B}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"70\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pendiente-dado-el-vector-director-de-la-recta\"><\/span> Kemiringan dengan memperhatikan vektor arah garis<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Vektor arah suatu garis adalah vektor yang menandai arahnya. Jadi, jika vektor arah suatu 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-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>\n<p> Kemiringan garis ini 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-cbe7689423f29f352d6a3def8b92e945_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<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pendiente-dado-un-angulo\"><\/span> kemiringan yang diberi sudut<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Terakhir, jika sebuah garis membentuk sudut<\/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-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> pada bagian positif sumbu absis (sumbu X), kemiringannya setara dengan garis singgung sudut: <\/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-c2b29dd45ad9f0c0537a0cf6233ce929_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<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"significado-de-la-pendiente-de-una-recta\"><\/span> Arti kemiringan suatu garis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dengan semua informasi di atas, kita sudah mengetahui betul cara mencari kemiringan suatu garis. Tapi sungguh\u2026 apa yang dimaksud dengan kemiringan suatu garis?<\/p>\n<p> <strong>Kemiringan suatu garis menunjukkan satuan vertikal yang ditinggikan garis tersebut untuk setiap satuan horizontal grafik.<\/strong><\/p>\n<p> Misalnya, pada representasi garis berikut, Anda dapat melihat bahwa garis tersebut maju 2 satuan vertikal untuk setiap satuan horizontal, karena kemiringannya sama dengan 2. <\/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\/equation-explicite-d-une-ligne.webp\" alt=\"berapa kemiringan suatu garis\" class=\"wp-image-1455\" width=\"341\" height=\"341\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Selain itu, kemiringan suatu garis juga menunjukkan kecuramannya:<\/p>\n<ul>\n<li> Jika suatu garis bertambah (naik), maka kemiringannya positif.<\/li>\n<li> Jika suatu garis menurun (menurun), kemiringannya negatif.<\/li>\n<li> Jika suatu garis benar-benar horizontal, kemiringannya sama dengan 0.<\/li>\n<li> Jika sebuah garis benar-benar vertikal, kemiringannya sama dengan tak terhingga. <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-167\">\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\/pente-positive-ou-negative-de-la-droite.webp\" alt=\"kemiringan garis positif atau negatif\" class=\"wp-image-1540\" width=\"470\" height=\"238\" 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\/pente-dune-ligne-zero-ou-infinie.webp\" alt=\"kemiringan garis nol atau tak terhingga\" class=\"wp-image-1541\" width=\"478\" height=\"238\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"posicion-relativa-de-las-rectas\"><\/span> Posisi relatif garis<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Sebaliknya kedudukan relatif antara dua garis juga dapat diketahui dari sifat-sifat lerengnya:<\/p>\n<ul>\n<li> Jika dua garis mempunyai kemiringan yang berbeda, berarti keduanya <strong>berpotongan<\/strong> , yaitu berpotongan di suatu titik. <\/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\/secantes-pente-d-une-ligne.webp\" alt=\"memotong garis lereng yang berbeda\" class=\"wp-image-1549\" width=\"222\" height=\"232\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Selain itu, sudut antara dua garis yang melintasi lerengnya dapat dihitung dengan 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-95b6b3d8558ce7ad38e9652a3f9f612d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tg}(\\alpha) = \\cfrac{m_2-m_1}{1+m_1\\cdot m_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"157\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<ul>\n<li> Kedua, jika dua garis memiliki kemiringan yang sama, berarti kedua garis tersebut <strong>sejajar<\/strong> . <\/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\/lignes-paralleles-pente-dune-ligne.webp\" alt=\"garis sejajar sama kemiringannya\" class=\"wp-image-1550\" width=\"207\" height=\"208\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<ul>\n<li> Terakhir, kemiringan dua garis <strong>tegak lurus<\/strong> atau <strong>ortogonal<\/strong> (yang membentuk 90\u00ba) memenuhi syarat 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\/lignes-perpendiculaires-pente-d-une-ligne.webp\" alt=\"garis tegak lurus terhadap lereng\" class=\"wp-image-1551\" width=\"183\" height=\"270\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Ini adalah salah satu cara untuk mengetahui apakah dua garis sejajar atau tegak lurus satu sama lain, namun ada cara lain dan bahkan ada yang lebih cepat. Untuk mengetahui lebih lanjut anda dapat menyimak penjelasan tentang <a href=\"https:\/\/mathority.org\/id\/pengertian-garis-tegak-lurus-dan-contoh-tegak-lurus\/\">tegak lurus<\/a> dan <a href=\"https:\/\/mathority.org\/id\/pengertian-garis-sejajar-dan-contohnya\/\">paralelisme antar garis<\/a> . Selain itu, halaman ini juga menjelaskan cara mencari garis yang tegak lurus (atau sejajar) dengan garis lainnya. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-pendiente-de-una-recta\"><\/span> Menyelesaikan masalah kemiringan suatu garis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Tentukan gradien 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-ae1737beb6850f4de1ea0c016cc1bc6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(5,6) \\qquad P_2(8,3)\" 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 menghitung kemiringan garis harus menggunakan 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-704148ba7570ada0ae582712ab7f93e6_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{3-6}{8-5}=\\cfrac{-3}{3} = \\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"316\" style=\"vertical-align: -15px;\"><\/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> Hitunglah 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-092707a43b0264500e478afcfe29aaea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(-3,1) \\qquad P_2(-2,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" 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 kemiringan garis harus menggunakan 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-96bd25846027e66360f0f5125603d20f_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{-4-1}{-2-(-3)}=\\cfrac{-5}{-2+3}=\\cfrac{-5}{1} = \\bm{-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"436\" 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> Berapakah kemiringan setiap garisnya? <\/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-5d405c8176957af59906c98149714570_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{lll} A) \\ y= 2x+3 &amp; \\qquad &amp; B) \\  y-3=4(x+1) \\\\[2ex] C) \\  6x+2y-7=0 &amp; \\qquad &amp; D) \\ \\begin{cases}x=3-t \\\\[2ex] y=1+2t \\end{cases} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"370\" 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\"> <strong>A)<\/strong> Garis tersebut dinyatakan sebagai persamaan implisit, sehingga <strong>kemiringannya adalah 2<\/strong> (suku yang menyertainya<\/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 class=\"has-text-align-left\"> <strong>B)<\/strong> Garis ditentukan oleh persamaan titik-kemiringannya, sehingga <strong>kemiringannya adalah 4<\/strong> (angka sebelum tanda kurung).<\/p>\n<p class=\"has-text-align-left\"> <strong>C)<\/strong> Garis tersebut berbentuk persamaan implisit, sehingga 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-0dd97ea88f88443fc8c46bde067053eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m= - \\cfrac{A}{B} = -\\cfrac{6}{2} = \\bm{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"164\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>D)<\/strong> Garis didefinisikan dalam bentuk persamaan parametrik, jadi kita harus mencari vektor arahnya terlebih dahulu dan dengan itu kita dapat menghitung kemiringan garis tersebut. Jadi, komponen vektor arah adalah suku-suku yang menyertai 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-40f8b062c79839dcf7f2885a9e1469e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" 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-920bbf7e23f9c991e14e800ec8003b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan setelah kita mengetahui vektor arah garis, kita dapat menentukan 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-62e1424e65bcd14a34c4b366789f7b3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\cfrac{\\text{v}_2}{\\text{v}_1} = \\cfrac{2}{-1} = \\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"152\" style=\"vertical-align: -15px;\"><\/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> Tentukan kemiringan setiap garis grafik: <\/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 <strong>kemiringannya sama dengan 1.<\/strong><\/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-d94dded0dc9c883f82d566d62e2d4b42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/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 <strong>kemiringannya adalah 3<\/strong> .<\/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\"> <strong>garis merah<\/strong><\/p>\n<p class=\"has-text-align-left\"> Garis merah berkurang dua Y untuk setiap X, sehingga <strong>kemiringannya sama dengan -2<\/strong> . <\/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<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan paling detail tentang kemiringan suatu garis: apa rumusnya, contoh perhitungannya, apa yang dimaksud dengan konsep kemiringan suatu garis,\u2026 Anda juga dapat melihat cara mudah mengidentifikasi kemiringan suatu garis. garis dari persamaannya dan, sebagai tambahan, Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. Rumus kemiringan suatu &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/kemiringan-rumus-garis\/\"> <span class=\"screen-reader-text\">Kemiringan suatu garis (rumus)<\/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-226","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>Kemiringan garis (rumus) - 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\/kemiringan-rumus-garis\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Kemiringan garis (rumus) - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan menemukan penjelasan paling detail tentang kemiringan suatu garis: apa rumusnya, contoh perhitungannya, apa yang dimaksud dengan konsep kemiringan suatu garis,\u2026 Anda juga dapat melihat cara mudah mengidentifikasi kemiringan suatu garis. garis dari persamaannya dan, sebagai tambahan, Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. 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