request dari siswa B. tolong ya.

1)
a.
[tex] m = \frac{y_2-y_1}{x_2-x_1} \\ m = \frac{4-6}{-1-0} \\ m = \frac{-2}{-1} \\ m = 2 [/tex]
b.
[tex] m = \frac{y_2-y_1}{x_2-x_1} \\ m = \frac{-1-5}{3-(-2)} \\ m = \frac{-6}{5} [/tex]

2)
a.
Gradien garis p
[tex] m_p = \frac{1-3}{2-(-1)} \\ m_p = \frac{-2}{3} [/tex]
b.
Garis p tegak lurus garis q maka,
[tex] m_p . m_q = -1 \\ \frac{-2}{3} . m_q = -1 \\ m_q = \frac{3}{2} \\ \frac{2-a}{2+a-4} = \frac{3}{2} \\ 2(2-a) = 3(a-2) \\ 4 - 2a = 3a - 6 \\ 10 = 5a \\ a = 2 [/tex]
c.
Dilampirkan pada gambar
Garis p merah, garis q oranye


3)
Garis (i) 5x - 6y + 2 = 0
6y = 5x + 2
y = [tex] \frac{5}{6}[/tex]x + [tex]\frac{1}{3}[/tex]
[tex] m_i = \frac{5}{6} [/tex]

Garis (ii) melalui (4,-3) dan tegak lurus garis (i)

[tex] m_i . m_ii = -1 \\ \frac{5}{6} . m_ii = -1 \\ m_ii = \frac{-6}{5} [/tex]

Masukkan ke persamaan garis y = mx + c, dengan (x,y) dari titik yg diketahui.

y = mx + c
[tex] -3 = \frac{-6}{5} . 4 + c \\ -3 = \frac{-24}{5} + c \\ c = \frac{9}{5} [/tex]

Jadi persamaan garis (ii) [tex] y = \frac{-6}{5}x + \frac{9}{5} [/tex].


4)
2x + 3y = 12

Titik potong sumbu X
y = 0
2x + 3.0 = 12
x = 6
Titiknya (6,0)

Titik potong sumbu Y
x = 0
2.0 + 3y = 12
y = 4
Titiknya (0,4)

Hubungkan kedua titik *gambar dilampirkan*
*warna biru*


5)
Persamaan garis
y = 5x - 3

Titik A (2,p), substitusi ke persamaan
p = 5.2 - 3
p = 7

Titik B (q,-3), substitusi ke persamaan
-3 = 5q - 3
0 = 5q
q = 0

1.
a. P(0, 6) dan Q(-1, 4)
x1 = 0
x2 = -1
y1 = 6
y2 = 4

m = (y2 - y1) / (x2 - x1)
m = (4 - 6) / (-1 - 0)
m = (-2)/(-1)
m = 2

b. C(-2, 5) dan D(3, -1)
x1 = -2
x2 = 3
y1 = 5
y2 = -1

m = (y2 - y1) / (x2 - x1)
m = (-1 - 5) / (3 - (-2))
m = (-6)/(5)
m = -6/5

2.
a. titik (-1,3) dan (2, 1)
x1 = -1
x2 = 2
y1 = 3
y2 = 1

m = (y2 - y1) / (x2 - x1)
m = (1 - 3) / (2 - (-1))
m = (-2)/(3)
m = -2/3

b. tegak lurus p
m1 = -2/3
m2 = 3/2

(4, a) dan (2+a, 2)
x1 = 4
x2 = 2+a
y1 = a
y2 = 2

m = (y2 - y1) / (x2 - x1)
3/2 = (2 - a) / (2+a - 4)
3/2 = (2 - a) / (a - 2)
2(2 - a) = 3(a - 2)
4 - 2a = 3a - 6
3a + 2a = 4 + 6
5a = 10
a = 2

3. melalui titik K(4, -3) tegak lurus 5x - 6y + 2 = 0
5x - 6y + 2 = 0
m = -a/b
m = -5/(-6)
m = 5/6

tegak lurus
m2 = -6/5

(y - y1) = m(x - x1)
(y - (-3)) = -6/5(x - 4)
(y + 3) = -6/5(x - 4)
----------------------------- kedua ruas dikali 5
5(y + 3) = -6(x - 4)
5y + 15 = -6x + 24
6x + 5y = 24 - 15
6x + 5y = 9

4.
2x + 3y = 12

titik potong sumbu x
y = 0
2x + 3(0) = 12
2x = 12
x = 6
titik potong (6, 0)

titik potong sumbu y
x = 0
2(0) + 3y = 12
3y = 12
y = 4
(0, 4)

5.
y = 5x - 3

A (2, p)
p = 5(2) - 3
p = 10 - 3
p = 7

B(q, -3)
-3 = 5(q) - 3
-3 = 5q - 3
5q = -3 + 3
5q = 0
q = 0