Pada artikel Matematika kelas 8 ini, kamu akan mempelajari cara mencari kemiringan (gradien) dari sebuah garis lurus disertai dengan masing-masing contoh soalnya.
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Siapa yang pernah naik pesawat terbang?
Tahukah kamu saat pesawat lepas landas (take off) atau ingin mendarat (landing), pesawat memerlukan kemiringan tertentu agar bisa terbang atau tiba di landasan dengan sempurna.
Nah, salah satu perhitungan matematika yang dapat diaplikasikan dalam menentukan kemiringan badan pesawat saat lepas landas atau mendarat akan kita bahas pada artikel kali ini. So, stay tuned, ya!
Coba deh kamu perhatikan gambar di atas. Jika kita anggap lintasan yang dilalui pesawat adalah suatu garis lurus, maka saat pesawat bergerak menuju udara, pesawat akan berjalan lurus ke atas dengan kemiringan tertentu. Begitu juga saat pesawat kembali menuju darat.
Apa itu Gradien?
Nah, kemiringan pada garis lurus ini dalam matematika disebut dengan gradien.
“Gradien adalah nilai yang menunjukkan kemiringan/kecondongan suatu garis lurus”
Umumnya, gradien disimbolkan dengan huruf “m”. Gradien akan menentukan seberapa miring suatu garis pada koordinat kartesius. Gradien suatu garis dapat miring ke kanan, miring ke kiri, curam, ataupun landai, tergantung dari nilai komponen X dan komponen Y nya.
Contoh macam-macam kemiringan (gradien) pada garis lurus dapat kamu lihat melalui gambar di bawah ini:
“Garis yang gradiennya positif akan miring ke kanan, sedangkan garis yang gradiennya negatif akan miring ke kiri”
Sekarang, kita coba cari tahu yuk mana garis yang gradiennya positif dan mana garis yang gradiennya negatif. Pada gambar nomor 1, ternyata garisnya miring ke kanan, sehingga dapat diketahui kalau gradiennya akan bernilai positif. Sementara itu, pada gambar nomor 4, garisnya miring ke kiri, sehingga gradiennya akan bernilai negatif.
Nah, kalau gambar nomor 2 dan 3, garisnya miring ke mana, ya? Kira-kira, gradiennya bernilai positif atau negatif? Hayoo… ada yang tau?
Baca Juga: Bagaimana Ya Cara Menentukan Persamaan Garis Lurus?
Oke, setelah kita mengetahui apa itu gradien suatu garis, materi yang akan kita bahas selanjutnya adalah bagaimana cara mencari nilai gradien tersebut. Wah, penasaran nggak, sih? Kalau gitu, langsung saja yuk kita simak!
—
Sebelum kita bahas tentang cara menentukan gradien garis lurus, kalo masih ada poin-poin yang belum kamu mengerti, mending belajar sama ahlinya, deh. Belajar bareng kakak-kakak pengajar di Ruangguru Privat Matematika misalnya.
Belajar nggak cuma menyenangkan, tapi kamu juga bakal diajari konsepnya sampai paham! Para pengajar di Ruangguru Privat juga sudah terstandarisasi kualitasnya, loh. Kamu juga bisa pilih nih, mau diajarkan secara langsung (offline) atau daring (online). Fleksibel, kan? Untuk info lebih lanjut, cuss klik link berikut!
Cara Menentukan Gradien Suatu Garis Lurus
Terdapat dua cara untuk mencari nilai gradien suatu garis yang bisa kamu ketahui, yaitu:
1. Jika diketahui bentuk persamaan garisnya
Secara umum, bentuk persamaan garis lurus ada dua macam, sehingga cara untuk menentukan gradiennya juga berbeda beda, tergantung dari bentuk persamaan garisnya.
a. Persamaan garis y = mx + c
Pada persamaan garis ini, gradien dapat dicari dengan mudah. Kenapa? Karena gradiennya adalah koefisien dari variabel x itu sendiri, yaitu m.
Contoh:
- Garis y = 3x + 2, koefisien x adalah 3. Jadi, gradien garis tersebut adalah 3.
- Garis y = -2x + 8, koefisien x adalah -2. Jadi, gradien garis tersebut adalah -2.
b. Persamaan garis ax + by + c = 0
Jika diketahui persamaan garis ax + by + c = 0, maka langkah pertama yang harus kamu lakukan adalah ubah persamaan garis tersebut ke bentuk y = mx + c, dengan m adalah gradien garis tersebut.
Di sini, kamu harus perhatikan tanda +/- dari koefisien masing-masing variabelnya, ya. Soalnya, tanda +/- akan berubah ketika kita pindah ruas persamaannya. Nah, kalau kamu merasa bingung, coba perhatikan contoh soal di bawah ini, ya.
Contoh:
1. Hitunglah kemiringan (gradien) pada persamaan garis berikut:
a) 5x + 2y – 8 = 0
b) 2x – 3y = 7
Penyelesaian:
a) Pertama-tama, kita ubah dulu persamaan 5x + 2y – 8 = 0 ke bentuk y = mx + c, sehingga persamaannya menjadi,
5x + 2y – 8 = 0
2y = -5x + 8
Koefisien x bernilai positif, yaitu 5, sehingga setelah kita pindah ruas ke kanan akan bernilai negatif. Begitu juga dengan konstanta -8 yang berubah tanda menjadi 8 karena pindah ruas ke kanan. Selanjutnya, kita bagi kedua ruas dengan 2.
y = (-5/2)x + 4
Jadi, gradien dari persamaan garis tersebut adalah -5/2.
Gimana? Kamu paham nggak sampai sini? Oke, supaya kamu semakin paham, coba kamu kerjakan contoh poin b. Terus, jawabannya kamu share deh di kolom komentar. Ditunggu ya jawabannya!
2. Jika diketahui dua titik yang dilalui garis
Jika diketahui dua titik yang dilalui suatu garis lurus, misalnya (x1,y1) dan (x2,y2), maka gradiennya dapat diperoleh dengan rumus m = ∆y/∆x = (y2-y1)/(x2-x1). Contoh soalnya seperti ini.
Contoh:
Perhatikan gambar berikut:
Gradien garis k pada gambar adalah…
Penyelesaian:
Diketahui dua buah titik yang dilalui oleh garis k, yaitu (4,0) dan (0,6). Misalnya kita pilih (x1,y1) = (4,0) dan (x2,y2) = (0,6), gradien garis tersebut dapat dicari menggunakan rumus m = ∆y/∆x = (y2-y1)/(x2-x1).
Jadi, gradien garis tersebut adalah -3/2. Di sini kamu bebas untuk memilih titik mana yang jadi (x1,y1) dan titik mana yang jadi (x2,y2) ya karena hasilnya akan sama saja.
Baca Juga: Belajar Sistem Koordinat Kartesius dan Cara Membuat Grafiknya, Yuk!
Wah, ternyata mudah ya untuk mencari kemiringan suatu garis? Rumusnya juga simpel lagi. Nah, untuk lebih memudahkan kamu dalam mengerjakan soal-soal tentang gradien, artikel ini sudah merangkup rumus-rumus di atas tadi, lho.
Tapi ingat, kamu jangan hanya hafal rumus-rumusnya saja, ya. Kamu juga harus pahami konsepnya. Caranya gimana? Kamu bisa identifikasi soalnya, apakah di soal diketahui persamaannya saja atau diketahui dua titik yang dilalui persamaan garis itu.
Biasanya sih, untuk cara nomor dua, soal yang disediakan berupa gambar grafik. Setelah itu, baru deh kamu bisa gunakan rumus-rumus yang sudah dijelaskan sebelumnya.
Cara mencari kemiringan (gradien) suatu garis lurus banyak sekali diterapkan untuk menyelesaikan berbagai masalah dalam kehidupan sehari-hari, lho.
Salah satunya, seperti yang sudah disebutkan di awal tadi, yaitu untuk memperhitungkan kemiringan badan pesawat saat lepas landas maupun mendarat. Bayangkan saja jika pilot tidak memperhitungkan kemiringan pesawat saat ingin mendarat, pasti jadinya bakal kayak gini:
Hiiiiiiyyy… serem banget, kan! (sumber: giphy.com)
Jadi, nggak ada alasan lagi buat kamu untuk malas belajar matematika dengan bilang kalau rumus matematika nggak ada manfaatnya sama sekali. Trust me, setiap ilmu yang kamu pelajari pasti ada manfaatnya!
Hubungan Antara Dua Garis Lurus
Oke, kita masuk ke materi yang terakhir ya, yaitu hubungan antara dua garis lurus. Hubungan dua garis lurus ini juga sangat penting untuk kamu ketahui karena biasanya untuk mencari gradien suatu garis akan bergantung dengan garis yang lain.
Gimana sih maksudnya? Untuk lebih jelasnya, coba kamu perhatikan gambar di bawah ini!
Baca Juga: Cara Mencari Rumus Pola Bilangan dan Contohnya, Pelajari Yuk!
Yuhuu… selesai sudah materi kita kali ini. Apakah kamu sudah paham tentang bagaimana cara mencari gradien garis lurus? Jika kamu ada pertanyaan, jangan ragu untuk menuliskannya di kolom komentar, ya.
Nah, kalau menurutmu materi ini kurang lengkap, kamu bisa lho belajar lebih dalam lagi di ruangbelajar. Selamat belajar, selamat meraih mimpi!
Referensi:
As’ari A.R, Tohir M, Valentino E, Imron Z, Taufiq I. (2017) Matematika SMP/MTs Kelas VIII Semester 1. Jakarta: Kementerian Pendidikan dan Kebudayaan
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<h1 class="content-title">
Cara Mencari Kemiringan (Gradien) pada Garis Lurus | Matematika Kelas 8 </h1>
<div class="content-meta">
<p class="content-author"><a href="https://www.ruangguru.com/blog/author/hani-ammariah" class="">Hani Ammariah</a> </p>
<p class="content-info"><span>February 23, 2026 • </span> <span>6 minutes read</span></p>
<br />
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<p><em><img decoding="async" style="height: auto; max-width: 100%; width: 820px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Cara%20Mencari%20Gradien%20Garis%20Lurus%20-%20Matematika%20Kelas%208-02.jpg" alt="Cara Mencari Gradien Garis Lurus - Matematika Kelas 8" /></em></p>
<blockquote>
<p style="text-align: center;"><em>Pada <a style="font-weight: bold;" href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-8" rel="noopener">artikel Matematika kelas 8</a> ini, kamu akan mempelajari cara mencari kemiringan (gradien) dari sebuah garis lurus disertai dengan masing-masing contoh soalnya.</em></p>
</blockquote>
<p style="text-align: center;"><em>—</em></p>
<p> </p>
<p style="text-align: justify;">Siapa yang pernah naik pesawat terbang?</p>
<p style="text-align: justify;">Tahukah kamu saat pesawat lepas landas (<em>take off</em>) atau ingin mendarat (<em>landing</em>), pesawat memerlukan kemiringan tertentu agar bisa terbang atau tiba di landasan dengan sempurna.</p>
<p style="text-align: justify;">Nah, salah satu perhitungan matematika yang dapat diaplikasikan dalam menentukan kemiringan badan pesawat saat lepas landas atau mendarat akan kita bahas pada artikel kali ini. <em>So, stay tuned</em>, ya!</p>
<p><img fetchpriority="high" decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Cara%20Mencari%20Gradien%20Garis%20Lurus%20-%20Matematika%20Kelas%208-03.jpg" alt="Cara Mencari Kemiringan Garis Lurus - Matematika Kelas 8" width="600" height="400" /></p>
<p> </p>
<p style="text-align: justify;">Coba deh kamu perhatikan gambar di atas. Jika kita anggap lintasan yang dilalui pesawat adalah suatu garis lurus, maka saat pesawat bergerak menuju udara, pesawat akan berjalan lurus ke atas dengan kemiringan tertentu. Begitu juga saat pesawat kembali menuju darat.</p>
<p> </p>
<h2><span style="font-size: 18pt;">Apa itu Gradien?</span></h2>
<p style="text-align: justify;">Nah, <span style="font-weight: bold;">kemiringan pada garis lurus ini dalam matematika disebut dengan gradien</span>.</p>
<blockquote>
<p style="font-weight: bold; text-align: center;"><span style="font-size: 14pt;"><em>“Gradien adalah nilai yang menunjukkan kemiringan/kecondongan suatu garis lurus”</em></span></p>
</blockquote>
<p> </p>
<p style="text-align: justify;">Umumnya, gradien disimbolkan dengan huruf “<strong>m</strong>”. Gradien akan menentukan seberapa miring suatu garis pada koordinat kartesius. Gradien suatu garis dapat miring ke kanan, miring ke kiri, curam, ataupun landai, tergantung dari nilai komponen X dan komponen Y nya.</p>
<p> </p>
<h2><span style="font-size: 18pt;">Contoh Gambar Gradien Garis Lurus</span></h2>
<p style="text-align: justify;">Contoh macam-macam kemiringan (gradien) pada garis lurus dapat kamu lihat melalui gambar di bawah ini:</p>
<p><img decoding="async" style="width: 512px; display: block; margin: 0px auto;" src="https://lh5.googleusercontent.com/BkLF6EUeYjcResiRXWxvszqrr-Du1C_tdIkX3sqFFfa4U-mzcibfcQsipxGpsaou9NydieFwslaPSO5K_8AQxqUZMSjJExvak3fu0mG_F9lOwsKKTtI4VAU8SN5fEgL2dN4cDNGP" alt="gambar rumus mencari gradien" width="512" /></p>
<blockquote>
<p style="font-weight: bold; text-align: center;"><span style="font-size: 14pt;"><em>“Garis yang gradiennya positif akan miring ke kanan, sedangkan garis yang gradiennya negatif akan miring ke kiri”</em></span></p>
</blockquote>
<p> </p>
<p style="text-align: justify;">Sekarang, kita coba cari tahu yuk mana garis yang gradiennya positif dan mana garis yang gradiennya negatif. Pada gambar nomor 1, ternyata garisnya miring ke kanan, sehingga dapat diketahui kalau gradiennya akan bernilai positif. Sementara itu, pada gambar nomor 4, garisnya miring ke kiri, sehingga gradiennya akan bernilai negatif.</p>
<p style="text-align: justify;">Nah, kalau gambar nomor 2 dan 3, garisnya miring ke mana, ya? Kira-kira, gradiennya bernilai positif atau negatif? <em>Hayoo</em>… ada yang tau?</p>
<p><img decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Cara%20Mencari%20Gradien%20Garis%20Lurus%20-%20Matematika%20Kelas%208-06.jpg" alt="Cara Mencari Gradien Garis Lurus - Penemu Kemiringan Garis - Rene Descartes - Matematika Kelas 8" width="600" height="400" /></p>
<p><strong>Baca Juga: <a href="/blog/matematika-kelas-8-cara-menentukan-persamaan-garis-lurus" rel="noopener">Bagaimana Ya Cara Menentukan Persamaan Garis Lurus?</a></strong></p>
<p> </p>
<p style="text-align: justify;">Oke, setelah kita mengetahui apa itu gradien suatu garis, materi yang akan kita bahas selanjutnya adalah bagaimana cara mencari nilai gradien tersebut. Wah, penasaran nggak, sih? Kalau gitu, langsung saja yuk kita simak!</p>
<p style="text-align: center;">—</p>
<p style="text-align: justify;">Sebelum kita bahas tentang cara menentukan gradien garis lurus, kalo masih ada poin-poin yang belum kamu mengerti, mending belajar sama ahlinya, deh. Belajar bareng kakak-kakak pengajar di <a href="https://www.ruangguru.com/privat/matematika"><strong>Ruangguru Privat Matematika</strong></a> misalnya.</p>
<p style="text-align: justify;">Belajar nggak cuma menyenangkan, tapi kamu juga bakal diajari konsepnya sampai paham! Para pengajar di Ruangguru Privat juga sudah terstandarisasi kualitasnya, loh. Kamu juga bisa pilih nih, mau diajarkan secara langsung (<em>offline</em>) atau daring (<em>online</em>). Fleksibel, kan? Untuk info lebih lanjut, cuss klik link berikut!</p>
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<p> </p>
<h2><span style="font-size: 18pt;">Cara Menentukan Gradien Suatu Garis Lurus</span></h2>
<p style="text-align: justify;">Terdapat dua cara untuk mencari nilai gradien suatu garis yang bisa kamu ketahui, yaitu:</p>
<p> </p>
<h3 style="font-size: 20px;"><span style="font-size: 14pt;">1. Jika diketahui bentuk persamaan garisnya</span></h3>
<p style="text-align: justify;">Secara umum, bentuk persamaan garis lurus ada dua macam, sehingga cara untuk menentukan gradiennya juga berbeda beda, tergantung dari bentuk persamaan garisnya.</p>
<p> </p>
<h4 style="text-align: justify; font-size: 16px;"><span style="background-color: transparent;">a. Persamaan garis </span><strong style="background-color: transparent;">y = mx + c</strong></h4>
<p style="text-align: justify;">Pada persamaan garis ini, gradien dapat dicari dengan mudah. Kenapa? Karena <strong>gradiennya adalah koefisien dari variabel x</strong> itu sendiri, yaitu m.</p>
<p><strong>Contoh:</strong></p>
<ol>
<li>Garis y = 3x + 2, koefisien x adalah 3. Jadi, gradien garis tersebut adalah 3.</li>
<li>Garis y = -2x + 8, koefisien x adalah -2. Jadi, gradien garis tersebut adalah -2.</li>
</ol>
<p> </p>
<h4 style="font-size: 16px;">b. Persamaan garis <strong>ax + by + c = 0</strong></h4>
<p style="text-align: justify;">Jika diketahui persamaan garis ax + by + c = 0, maka langkah pertama yang harus kamu lakukan adalah <strong>ubah persamaan garis tersebut ke bentuk y = mx + c</strong>, dengan <strong>m adalah gradien garis tersebut</strong>.</p>
<p style="text-align: justify;">Di sini, kamu harus perhatikan tanda +/- dari koefisien masing-masing variabelnya, ya. Soalnya, tanda +/- akan berubah ketika kita pindah ruas persamaannya. <em>Nah</em>, kalau kamu merasa bingung, coba perhatikan contoh soal di bawah ini, ya.</p>
<p><strong>Contoh:</strong></p>
<p>1. Hitunglah kemiringan (gradien) pada persamaan garis berikut:</p>
<p style="text-align: left;"><span style="background-color: transparent;">a) 5x + 2y – 8 = 0</span></p>
<p style="text-align: left;"><span style="background-color: transparent;">b) 2x – 3y = 7</span></p>
<p><strong>Penyelesaian:</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">a) Pertama-tama, kita ubah dulu persamaan 5x + 2y – 8 = 0 ke bentuk y = mx + c, sehingga persamaannya menjadi,</span></p>
<p style="text-align: center;">5x + 2y – 8 = 0</p>
<p style="text-align: center;">2y = -5x + 8</p>
<p style="text-align: justify;">Koefisien x bernilai positif, yaitu 5, sehingga setelah kita pindah ruas ke kanan akan bernilai negatif. Begitu juga dengan konstanta -8 yang berubah tanda menjadi 8 karena pindah ruas ke kanan. Selanjutnya, kita bagi kedua ruas dengan 2.</p>
<p style="text-align: center;">y = (-5/2)x + 4</p>
<p>Jadi, gradien dari persamaan garis tersebut adalah -5/2.</p>
<p style="text-align: justify;">Gimana? Kamu paham nggak sampai sini? Oke, supaya kamu semakin paham, coba kamu kerjakan contoh poin b. Terus, jawabannya kamu <em>share</em> deh di kolom komentar. Ditunggu ya jawabannya!</p>
<p> </p>
<h3 style="font-size: 20px;"><span style="font-size: 14pt;">2. Jika diketahui dua titik yang dilalui garis</span></h3>
<p style="text-align: justify;">Jika diketahui dua titik yang dilalui suatu garis lurus, misalnya (x<sub>1</sub>,y<sub>1</sub>) dan (x<sub>2</sub>,y<sub>2</sub>), maka gradiennya dapat diperoleh dengan rumus <strong>m = ∆y/∆x = (y<sub>2</sub>-y<sub>1</sub>)/(x<sub>2</sub>-x<sub>1</sub>)</strong>. Contoh soalnya seperti ini.</p>
<p><strong>Contoh:</strong></p>
<p>Perhatikan gambar berikut:</p>
<p><img decoding="async" style="width: 337px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/gradien%205.png" alt="rumus mencari gradien" width="337" /></p>
<p>Gradien garis k pada gambar adalah…</p>
<p><strong>Penyelesaian:</strong></p>
<p style="text-align: justify;">Diketahui dua buah titik yang dilalui oleh garis k, yaitu (4,0) dan (0,6). Misalnya kita pilih (x<sub>1</sub>,y<sub>1</sub>) = (4,0) dan (x<sub>2</sub>,y<sub>2</sub>) = (0,6), gradien garis tersebut dapat dicari menggunakan rumus m = ∆y/∆x = (y<sub>2</sub>-y<sub>1</sub>)/(x<sub>2</sub>-x<sub>1</sub>).</p>
<p><img decoding="async" style="width: 186px; display: block; margin-left: auto; margin-right: auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/gradien%206.png" alt="rumus mencari gradien pada garis lurus" width="186" /></p>
<p style="text-align: justify;">Jadi, gradien garis tersebut adalah -3/2. Di sini kamu bebas untuk memilih titik mana yang jadi (x<sub>1</sub>,y<sub>1</sub>) dan titik mana yang jadi (x<sub>2</sub>,y<sub>2</sub>) ya karena hasilnya akan sama saja.</p>
<p><strong>Baca Juga: <a href="/blog/sistem-koordinat-kartesius-dan-cara-membuat-grafiknya-matematika-kelas-8" rel="noopener">Belajar Sistem Koordinat Kartesius dan Cara Membuat Grafiknya, Yuk!</a></strong></p>
<p style="text-align: justify;"><em>Wah</em>, ternyata mudah ya untuk mencari kemiringan suatu garis? Rumusnya juga simpel lagi. <em>Nah</em>, untuk lebih memudahkan kamu dalam mengerjakan soal-soal tentang gradien, artikel ini sudah merangkup rumus-rumus di atas tadi, <em>lho</em>.</p>
<p><img decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Cara%20Mencari%20Gradien%20Garis%20Lurus%20-%20Matematika%20Kelas%208-04.jpg" alt="Rumus Gradien Garis Lurus - Matematika Kelas 8" width="600" height="600" /></p>
<p> </p>
<p style="text-align: justify;">Tapi ingat, kamu jangan hanya hafal rumus-rumusnya saja, ya. Kamu juga harus pahami konsepnya. Caranya gimana? Kamu bisa identifikasi soalnya, apakah di soal diketahui persamaannya saja atau diketahui dua titik yang dilalui persamaan garis itu.</p>
<p style="text-align: justify;">Biasanya sih, untuk cara nomor dua, soal yang disediakan berupa gambar grafik. Setelah itu, baru <i>deh</i> kamu bisa gunakan rumus-rumus yang sudah dijelaskan sebelumnya.</p>
<p style="text-align: justify;">Cara mencari kemiringan (gradien) suatu garis lurus banyak sekali diterapkan untuk menyelesaikan berbagai masalah dalam kehidupan sehari-hari, lho.</p>
<p style="text-align: justify;">Salah satunya, seperti yang sudah disebutkan di awal tadi, yaitu untuk memperhitungkan kemiringan badan pesawat saat lepas landas maupun mendarat. Bayangkan saja jika pilot tidak memperhitungkan kemiringan pesawat saat ingin mendarat, pasti jadinya bakal kayak gini:</p>
<p style="text-align: center;"><img loading="lazy" decoding="async" style="width: 600px; display: block; margin: 0px auto; height: auto; max-width: 100%;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/giphy%20(18).gif" alt="rumus mencari gradien" width="600" height="450" /></p>
<p style="text-align: center;"><em>Hiiiiiiyyy… serem banget, kan! (sumber: giphy.com)</em></p>
<p> </p>
<p style="text-align: justify;">Jadi, nggak ada alasan lagi buat kamu untuk malas belajar matematika dengan bilang kalau rumus matematika nggak ada manfaatnya sama sekali. <em>Trust me</em>, setiap ilmu yang kamu pelajari pasti ada manfaatnya!</p>
<p> </p>
<h2><span style="font-size: 18pt;">Hubungan Antara Dua Garis Lurus</span></h2>
<p style="text-align: justify;">Oke, kita masuk ke materi yang terakhir ya, yaitu hubungan antara dua garis lurus. Hubungan dua garis lurus ini juga sangat penting untuk kamu ketahui karena biasanya untuk mencari gradien suatu garis akan bergantung dengan garis yang lain.</p>
<p style="text-align: justify;">Gimana sih maksudnya? Untuk lebih jelasnya, coba kamu perhatikan gambar di bawah ini!</p>
<p><img loading="lazy" decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Cara%20Mencari%20Gradien%20Garis%20Lurus%20-%20Matematika%20Kelas%208-05.jpg" alt="Cara Mencari Gradien Garis Lurus - Hubungan Dua Garis Lurus dengan Gradien - Matematika Kelas 8" width="600" height="600" /></p>
<p><strong>Baca Juga: <a href="/blog/cara-mencari-pola-bilangan" rel="noopener">Cara Mencari Rumus Pola Bilangan dan Contohnya, Pelajari Yuk!</a></strong></p>
<p> </p>
<p style="text-align: justify;"><em>Yuhuu</em>… selesai sudah materi kita kali ini. Apakah kamu sudah paham tentang bagaimana cara mencari gradien garis lurus? Jika kamu ada pertanyaan, jangan ragu untuk menuliskannya di kolom komentar, ya.</p>
<p style="text-align: justify;">Nah, kalau menurutmu materi ini kurang lengkap, kamu bisa lho belajar lebih dalam lagi di <strong><a href="https://www.ruangguru.com/ruangbelajar" rel="noopener">ruangbelajar</a></strong>. Selamat belajar, selamat meraih mimpi!</p>
<p><a href="https://app.ruangguru.com/ruangbelajar/"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/a2dbab8e-e903-4b70-ae04-39ff5807647e.jpg" alt="CTA ruangbelajar" /></a></p>
<p><strong>Referensi:</strong></p>
<p style="text-align: left;">As’ari A.R, Tohir M, Valentino E, Imron Z, Taufiq I. (2017) Matematika SMP/MTs Kelas VIII Semester 1. Jakarta: Kementerian Pendidikan dan Kebudayaan</p>
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<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>