SOAL & KUNCI JAWABAN Pelajaran Matematika Kelas 8 Hal 181-188, Gambar Grafik Persamaan Garis Lurus

a) m = (y - y1) / (x - x1)
= (3 - (-5)) / (4 - (-2))
= 8 / 6

= 4/3

b) m = (y - y1) / (x - x1)
= (-1 - (-3)) / (-1 - (7))
= 2 / -8
= -1/4

3. Tentukan persamaan garis lurus jika diketahui informasi berikut.

Jawaban :

a) y - b = m(x - a)
y + 4 = 3(x - 0)
y + 4 = 3x
3x - y - 4 = 0

b) y - 2 = (- 3/2)(x - 1)
2y - 4 = - 3x + 3
3x + 2y - 7 = 0

c) y - 1 = 4(x + 2)
y - 1 = 4x + 8
4x - y + 9 = 0

d) (y - y1) / (y2 - y1) = (x - x1) / (x2 - x1)
(y - 4) / (-1 -4) = (x - 1) / (2 - 1)
(y - 4) / -5 = (x - 1) / 1
y - 4 = -5x + 5
5x + y - 9 = 0

e) (y - y1) / (y2 - y1) = (x - x1) / (x2 - x1)
(y - 0) / (-8 - 0) = (x + 1) / (3 + 1)
y / -8 = (x + 1) / 4
4y = -8x -8
8x + 4y + 8 = 0
2x + y + 2 = 0

4. Titik P, Q, dan R berturut-turut berkoordinat di (0, 2), (5, 0) dan (3, 4).

Jawaban :

a) m = (0 - 2) / (5 - 0) = -2/5
y - y1 = m (x - x1)
y - 4 = -2/5 (x - 3)
5y - 20 = -2x + 6
2x + 5y - 26 = 0

b) (i) y - y₁ = m(x - x₁)
y - 4 = 2(x - 3)
y - 4 = 2x - 6
y = 2x - 6 + 4
y = 2x - 2

(ii) Karena memotong sumbu y maka, x = 0, y = 2(0) - 2 y = -2
Jadi, koordinat titik S(0, -2)