{"id":304614,"date":"2021-11-01T00:00:04","date_gmt":"2021-10-31T17:00:04","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=304614"},"modified":"2022-10-14T14:26:42","modified_gmt":"2022-10-14T07:26:42","slug":"persamaan-garis-lurus","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/persamaan-garis-lurus\/","title":{"rendered":"Pengertian Persamaan Garis Lurus &#8211; Rumus, Grafik dan Soal"},"content":{"rendered":"\n<figure class=\"wp-block-image\"><img fetchpriority=\"high\" decoding=\"async\" width=\"800\" height=\"533\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Persamaan-Garis-Lurus.webp\" alt=\"\" class=\"wp-image-304644\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Persamaan-Garis-Lurus.webp 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Persamaan-Garis-Lurus-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Persamaan-Garis-Lurus-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Persamaan-Garis-Lurus-263x175.webp?crop=1 263w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Dalam dunia konstruksi, posisi bangunan menjadi hal utama yang harus diperhatikan. Bahkan, tingkat kemiringan bangunan tidak bisa diabaikan karena bisa berpengaruh pada kekokohannya. Nah, membahas masalah kemiringan tentu tidak akan lepas dari persamaan garis lurus. Ingin tahu selengkapnya? <\/span><em><span style=\"font-weight: 400;\">Check this out<\/span><\/em><span style=\"font-weight: 400;\">!<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Pengertian Persamaan Garis Lurus<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Persamaan garis lurus adalah persamaan yang memuat satu atau lebih variabel, di mana masing-masing variabelnya berpangkat satu.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika persamaan tersebut dilukiskan dalam diagram Cartesius, akan terbentuk grafik garis lurus dengan kemiringan tertentu. Kemiringan itu biasa disebut gradien garis (<\/span><em><span style=\"font-weight: 400;\">m<\/span><\/em><span style=\"font-weight: 400;\">).<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Bentuk Persamaan Garis&nbsp;<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Secara umum, persamaan garis lurus memiliki dua bentuk yaitu sebagai berikut.<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1. Bentuk eksplisit<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Bentuk eksplisit adalah bentuk persamaan garis yang memenuhi <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> = <\/span><em><span style=\"font-weight: 400;\">mx<\/span><\/em><span style=\"font-weight: 400;\"> + <\/span><em><span style=\"font-weight: 400;\">c<\/span><\/em><span style=\"font-weight: 400;\">, dengan <\/span><em><span style=\"font-weight: 400;\">m<\/span><\/em><span style=\"font-weight: 400;\"> = gradien garis dan <\/span><em><span style=\"font-weight: 400;\">c<\/span><\/em><span style=\"font-weight: 400;\"> = konstanta.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Adapun contoh bentuk eksplisit adalah <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> = 3<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> + 6. Berdasarkan persamaan tersebut, gradien garisnya = 3.&nbsp;<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>2. Bentuk implisit<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Bentuk implisit adalah bentuk persamaan garis yang memenuhi <\/span><em><span style=\"font-weight: 400;\">Ax<\/span><\/em><span style=\"font-weight: 400;\"> + <\/span><em><span style=\"font-weight: 400;\">By<\/span><\/em><span style=\"font-weight: 400;\"> + <\/span><em><span style=\"font-weight: 400;\">c<\/span><\/em><span style=\"font-weight: 400;\"> = 0. Adapun contoh bentuk implisit adalah 3<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> \u2013 <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> + 6 = 0.&nbsp;<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"585\" height=\"97\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-a.webp\" alt=\"\" class=\"wp-image-304640\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika digambarkan dalam diagram Cartesius, grafik persamaan garis lurus <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> = 3<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> + 6 atau 3<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> \u2013 <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> + 6 = 0 adalah sebagai berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"418\" height=\"433\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-b.webp\" alt=\"\" class=\"wp-image-304639\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Cara Mencari Gradien<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Sebelum mencari persamaan garis, Quipperian harus tahu dulu cara menentukan gradien garisnya. Inilah beberapa cara untuk menentukan gradien garis.<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1. Gradien garis yang melalui dua titik<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika sebuah garis lurus melalui dua titik koordinat <\/span><em><span style=\"font-weight: 400;\">A<\/span><\/em><span style=\"font-weight: 400;\">(<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><sub><span style=\"font-weight: 400;\">1<\/span><\/sub><span style=\"font-weight: 400;\">,<\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><sub><span style=\"font-weight: 400;\">1<\/span><\/sub><span style=\"font-weight: 400;\">) dan <\/span><em><span style=\"font-weight: 400;\">B<\/span><\/em><span style=\"font-weight: 400;\">(<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><sub><span style=\"font-weight: 400;\">2<\/span><\/sub><span style=\"font-weight: 400;\">,<\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><sub><span style=\"font-weight: 400;\">2<\/span><\/sub><span style=\"font-weight: 400;\">), maka gradiennya merupakan hasil bagi antara selisih nilai ordinat dan absisnya.&nbsp;<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"434\" height=\"427\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-c.webp\" alt=\"\" class=\"wp-image-304638\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Secara matematis, dirumuskan sebagai berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"161\" height=\"89\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-d.webp\" alt=\"\" class=\"wp-image-304637\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tentukan gradien garis yang melalui titik <\/span><em><span style=\"font-weight: 400;\">A<\/span><\/em><span style=\"font-weight: 400;\">(-3,2) dan <\/span><em><span style=\"font-weight: 400;\">B<\/span><\/em><span style=\"font-weight: 400;\">(-2,5)!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tentukan dahulu nilai (<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><sub><span style=\"font-weight: 400;\">1<\/span><\/sub><span style=\"font-weight: 400;\">,<\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><sub><span style=\"font-weight: 400;\">1<\/span><\/sub><span style=\"font-weight: 400;\">) dan (<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><sub><span style=\"font-weight: 400;\">2<\/span><\/sub><span style=\"font-weight: 400;\">,<\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><sub><span style=\"font-weight: 400;\">2<\/span><\/sub><span style=\"font-weight: 400;\">)nya.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em><span style=\"font-weight: 400;\">x<\/span><\/em><sub><span style=\"font-weight: 400;\">1<\/span><\/sub><span style=\"font-weight: 400;\"> = -3<\/span><\/li>\n\n\n\n<li><em><span style=\"font-weight: 400;\">y<\/span><\/em><sub><span style=\"font-weight: 400;\">1<\/span><\/sub><span style=\"font-weight: 400;\"> = 2<\/span><\/li>\n\n\n\n<li><em><span style=\"font-weight: 400;\">x<\/span><\/em><sub><span style=\"font-weight: 400;\">2<\/span><\/sub><span style=\"font-weight: 400;\"> = -2<\/span><\/li>\n\n\n\n<li><em><span style=\"font-weight: 400;\">y<\/span><\/em><sub><span style=\"font-weight: 400;\">2<\/span><\/sub><span style=\"font-weight: 400;\"> = 5<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Untuk menentukan gradien garisnya, gunakan persamaan berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"168\" height=\"181\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-e.webp\" alt=\"\" class=\"wp-image-304636\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, gradien garisnya adalah 3.<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>2. Gradien tegak lurus<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika dua garis saling tegak lurus, maka hasil kali gradien kedua garis tersebut sama dengan -1.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"460\" height=\"321\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-f.webp\" alt=\"\" class=\"wp-image-304635\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Mari kita buktikan!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Gradien garis k<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"142\" height=\"130\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-g.webp\" alt=\"\" class=\"wp-image-304634\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Gradien garis h<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"131\" height=\"107\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-h.webp\" alt=\"\" class=\"wp-image-304633\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Hubungan antara gradien garis k dan garis h adalah<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"278\" height=\"65\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-i.webp\" alt=\"\" class=\"wp-image-304632\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Dengan demikian, terbukti bahwa hasil kali gradien kedua garis tersebut adalah -1. Secara matematis, rumus gradien tegak lurus dirumuskan sebagai berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"138\" height=\"71\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-j.webp\" alt=\"\" class=\"wp-image-304631\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Dengan:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em><span style=\"font-weight: 400;\">m<\/span><\/em><sub><em><span style=\"font-weight: 400;\">1<\/span><\/em><\/sub> <span style=\"font-weight: 400;\">= gradien garis ke-1; dan<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em><span style=\"font-weight: 400;\">m<\/span><\/em><sub><em><span style=\"font-weight: 400;\">2<\/span><\/em><\/sub><span style=\"font-weight: 400;\"> = gradien garis ke-2.<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3. Gradien garis yang saling sejajar<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika dua garis sama-sama sejajar, maka gradien kedua garis tersebut sama.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"572\" height=\"539\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-k.webp\" alt=\"\" class=\"wp-image-304630\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Mari kita buktikan!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Gradien garis p<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"152\" height=\"126\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-l.webp\" alt=\"\" class=\"wp-image-304629\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\"> <\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Gradien garis q<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"117\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-m.webp\" alt=\"\" class=\"wp-image-304628\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\"> <\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Berdasarkan perhitungan, terbukti bahwa gradien garis p dan q adalah sama. Secara matematis, rumus gradien garis yang saling sejajar adalah sebagai berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"105\" height=\"55\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-n.webp\" alt=\"\" class=\"wp-image-304627\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Cara Mencari Persamaan Garis<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Setelah sebelumnya Quipperian belajar bagaimana cara menentukan gradien garis, kini saatnya belajar bagaimana <\/span><em><span style=\"font-weight: 400;\">sih<\/span><\/em><span style=\"font-weight: 400;\"> cara mencari persamaan garis itu. Ada beberapa cara untuk mencarinya, yaitu sebagai berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Persamaan garis lurus melalui titik (<em>x<\/em><sub><em>1<\/em><\/sub>,<em>y<\/em><sub><em>1<\/em><\/sub>) dan bergradien <em>m<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika sebuah garis yang bergradien <\/span><em><span style=\"font-weight: 400;\">m<\/span><\/em><span style=\"font-weight: 400;\"> melalui titik&nbsp; (<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><sub><em><span style=\"font-weight: 400;\">1<\/span><\/em><\/sub><span style=\"font-weight: 400;\">,<\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><sub><em><span style=\"font-weight: 400;\">1<\/span><\/em><\/sub><span style=\"font-weight: 400;\">), rumus persamaan garis lurusnya adalah sebagai berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"163\" height=\"58\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-o.webp\" alt=\"\" class=\"wp-image-304626\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><span style=\"text-decoration: underline;\">Perhatikan contoh berikut.<\/span><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tentukan persamaan garis lurus yang melalui titik (6,-2) dan bergradien 2.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Adapun nilai <\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><sub><em><span style=\"font-weight: 400;\">1<\/span><\/em><\/sub><span style=\"font-weight: 400;\"> = 6 dan <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><sub><em><span style=\"font-weight: 400;\">1<\/span><\/em><\/sub><span style=\"font-weight: 400;\"> = -2, <\/span><em><span style=\"font-weight: 400;\">m<\/span><\/em><span style=\"font-weight: 400;\"> = 2.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Dengan demikian, persamaan garis lurusnya adalah sebagai berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"190\" height=\"137\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-p.webp\" alt=\"\" class=\"wp-image-304625\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, persamaan garisnya adalah <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> = 2<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> \u2013 10.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Persamaan garis lurus melalui 2 titik, yaitu <em>A<\/em>(<em>x<\/em><sub>1<\/sub>,<em>y<\/em><sub>1<\/sub>) dan <em>B<\/em>(<em>x<\/em><sub>2<\/sub>,<em>y<\/em><sub>2<\/sub>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika sebuah garis lurus melalui 2 titik <\/span><em><span style=\"font-weight: 400;\">A<\/span><\/em><span style=\"font-weight: 400;\">(<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">,<\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">) dan <\/span><em><span style=\"font-weight: 400;\">B<\/span><\/em><span style=\"font-weight: 400;\">(<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">,<\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">), maka persamaan garisnya ditentukan dengan rumus berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"155\" height=\"75\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-q.webp\" alt=\"\" class=\"wp-image-304624\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\"> <\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"text-decoration: underline;\"><strong>Perhatikan contoh berikut.<\/strong><\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tentukan persamaan garis yang melalui titik <\/span><em><span style=\"font-weight: 400;\">P<\/span><\/em><span style=\"font-weight: 400;\">(4,-2) dan <\/span><em><span style=\"font-weight: 400;\">Q<\/span><\/em><span style=\"font-weight: 400;\">(-1,3)!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Untuk mencari persamaan garisnya, gunakan persamaan berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"175\" height=\"220\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-r.webp\" alt=\"\" class=\"wp-image-304623\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, persamaan garis lurus yang melalui titik <\/span><em><span style=\"font-weight: 400;\">P<\/span><\/em><span style=\"font-weight: 400;\">(4,-2) dan <\/span><em><span style=\"font-weight: 400;\">Q<\/span><\/em><span style=\"font-weight: 400;\">(-1,3) adalah <\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> + <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> \u2013 2 = 0.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3. Persamaan garis lurus saling sejajar<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika diketahui suatu garis sejajar dengan garis lain yang persamaannya diketahui, maka Quipperian harus mencari dahulu gradien garis yang diketahui persamaannya tersebut. Lalu, substitusikan nilai gradien tersebut ke persamaan berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"145\" height=\"46\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-s.webp\" alt=\"\" class=\"wp-image-304622\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Agar kamu lebih memahaminya, perhatikan contoh soal berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Garis A melalui titik (4,-1) dan sejajar dengan garis B yang persamaannya <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> = 2<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> + 5. Tentukan persamaan garis A!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pertama, tentukan gradien garis B<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"475\" height=\"237\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-t.webp\" alt=\"\" class=\"wp-image-304621\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, persamaan garis A adalah <\/span><i><span style=\"font-weight: 400;\">y<\/span><\/i><span style=\"font-weight: 400;\"> = 2<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> \u2013 9.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">4. Persamaan garis lurus yang saling tegak lurus<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pada prinsipnya, caranya sama dengan dua garis yang saling sejajar, yaitu dengan mencari gradien salah satu garisnya. Lalu, lakukan perkalian hingga menghasilkan nilai -1.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"573\" height=\"113\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-u.webp\" alt=\"\" class=\"wp-image-304620\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pertama, tentukan gradien garis Q.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"496\" height=\"382\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-v.webp\" alt=\"\" class=\"wp-image-304619\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, persamaan garis P adalah <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> = -2<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\">.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Bagaimana Quipperian, apakah sudah paham dengan materi kali ini? Untuk mengasah pemahamanmu, perhatikan contoh soal berikut ini.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh Soal 1<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Gambarkan grafik garis lurus yang memiliki persamaan 4<\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> \u2013 2<\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> + 8 = 0.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pertama, Quipperian harus melakukan analisis titik koordinat mana saja yang dilalui garis tersebut. Asumsikan saat <\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> = 0 dan <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> = 0.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Jika <\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> = 0, maka <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> = 4, sehingga titik koordinatnya (0,4)<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Jika <\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> = 0, maka <\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> = -2, sehingga titik koordinatnya (-2,0)<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Gambar garis lurusnya.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"440\" height=\"417\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-w.webp\" alt=\"\" class=\"wp-image-304618\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh Soal 2<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">&nbsp;Sebuah fungsi permintaan memiliki persamaan <\/span><em><span style=\"font-weight: 400;\">P <\/span><\/em><span style=\"font-weight: 400;\">= -3<\/span><em><span style=\"font-weight: 400;\">Q<\/span><\/em><span style=\"font-weight: 400;\"> + 15. Tentukan banyaknya permintaan tertinggi beserta gambar grafiknya.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Permintaan tertinggi dipenuhi jika <\/span><em><span style=\"font-weight: 400;\">P<\/span><\/em><span style=\"font-weight: 400;\"> = 0. Artinya, Quipperian harus mencari nilai <\/span><em><span style=\"font-weight: 400;\">Q<\/span><\/em><span style=\"font-weight: 400;\"> saat <\/span><em><span style=\"font-weight: 400;\">P<\/span><\/em><span style=\"font-weight: 400;\"> = 0.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em><span style=\"font-weight: 400;\">P <\/span><\/em><span style=\"font-weight: 400;\">= -3<\/span><em><span style=\"font-weight: 400;\">Q<\/span><\/em><span style=\"font-weight: 400;\"> + 15<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">\u2194<\/span><span style=\"font-weight: 400;\"> 0 = -3<\/span><em><span style=\"font-weight: 400;\">Q<\/span><\/em><span style=\"font-weight: 400;\"> + 15<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">\u2194<\/span><span style=\"font-weight: 400;\"> 3<\/span><em><span style=\"font-weight: 400;\">Q<\/span><\/em><span style=\"font-weight: 400;\"> = 15<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">\u2194<\/span> <em><span style=\"font-weight: 400;\">Q<\/span><\/em><span style=\"font-weight: 400;\"> = 5<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, permintaan tertingginya adalah 5 unit.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Gambar garis lurus:<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Jika <\/span><em><span style=\"font-weight: 400;\">P<\/span><\/em><span style=\"font-weight: 400;\"> = 0, maka <\/span><em><span style=\"font-weight: 400;\">Q<\/span><\/em><span style=\"font-weight: 400;\"> = 5<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Jika <\/span><em><span style=\"font-weight: 400;\">Q<\/span><\/em><span style=\"font-weight: 400;\"> = 0, maka <\/span><em><span style=\"font-weight: 400;\">P<\/span><\/em><span style=\"font-weight: 400;\"> = 15<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Berikut ini gambar garisnya.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"425\" height=\"429\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-x.webp\" alt=\"\" class=\"wp-image-304617\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh Soal 3<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Di bawah ini yang termasuk persamaan garis lurus adalah\u2026.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"176\" height=\"168\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Persamaan-Garis-Lurus-y.webp\" alt=\"\" class=\"wp-image-304616\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Kamu harus ingat bahwa persamaan garis lurus memuat variabel yang berpangkat 1. Dari ketiga persamaan pada soal, jelas bahwa persamaan yang termasuk persamaan garis lurus adalah <\/span><em><span style=\"font-weight: 400;\">x<\/span><\/em><span style=\"font-weight: 400;\"> \u2013 10<\/span><em><span style=\"font-weight: 400;\">y<\/span><\/em><span style=\"font-weight: 400;\"> \u2013 21 = 0.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Itulah pembahasan Quipper Blog kali ini. Semoga bisa bermanfaat buat Quipperian. Jika kamu ingin mendapatkan materi lengkapnya, yuk buruan gabung <\/span><a href=\"https:\/\/subscribe.quipper.com\/signup\"><strong>Quipper Video<\/strong><\/a><span style=\"font-weight: 400;\">. Bersama Quipper Video, belajar jadi semakin mudah dan menyenangkan. Salam Quipper!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Penulis: Eka Viandari<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dalam dunia konstruksi, posisi bangunan menjadi hal utama yang harus diperhatikan. Bahkan, tingkat kemiringan bangunan tidak bisa diabaikan karena bisa berpengaruh pada kekokohannya. Nah,&hellip;<\/p>\n","protected":false},"author":99400369,"featured_media":304644,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679384865],"tags":[],"ppma_author":[679386827],"class_list":["post-304614","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pengertian Persamaan Garis Lurus - Rumus, Grafik dan Soal - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Belajar materi Persamaan Garis Lurus meliputi pengertian, rumus gradian sebelum mencari persamaan garis lurus, grafik dan contoh soal\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/persamaan-garis-lurus\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pengertian Persamaan Garis Lurus - Rumus, Grafik dan Soal - Quipper Blog\" \/>\n<meta property=\"og:description\" content=\"Belajar materi Persamaan Garis Lurus meliputi pengertian, rumus gradian sebelum mencari persamaan garis lurus, grafik dan contoh soal\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/persamaan-garis-lurus\/\" \/>\n<meta property=\"og:site_name\" content=\"Quipper Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/QuipperVideoID\/\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-31T17:00:04+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-10-14T07:26:42+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Persamaan-Garis-Lurus.webp\" \/>\n\t<meta property=\"og:image:width\" content=\"800\" \/>\n\t<meta property=\"og:image:height\" content=\"533\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/webp\" \/>\n<meta name=\"author\" content=\"sereliciouz\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@quipper_id\" \/>\n<meta name=\"twitter:site\" content=\"@quipper_id\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"sereliciouz\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.quipper.com\\\/id\\\/blog\\\/mapel\\\/matematika\\\/persamaan-garis-lurus\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/persamaan-garis-lurus\\\/\"},\"author\":{\"name\":\"sereliciouz\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#\\\/schema\\\/person\\\/b08224c7b72a87b156db30c3b032083b\"},\"headline\":\"Pengertian Persamaan Garis Lurus &#8211; 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