Explanation:
Number 1
For parallelism.....
gradient of the two lines is the same
y = 3/2x -4
y = mx + C
m = 3/2
(-1, 0) = (x1, y1)
y - y1 = m(x - x1)
y - 0 = 3/2[x - (-1)]
y = 3/2(x + 1)
2y = 3x + 3
y = 3/2x + 3/2
Option A
Number 2
For parallelism.....
gradient of the two lines is the same
y = -½x + 2
y = mx + c
m = -½
(-2, -1) = (x1, y1)
y - y1 = m(x - x1)
y - (-1) = -½[x - (-2)]
y + 1 = -½(x + 2)
2(y + 1) = -(x + 2)
2y + 2 = -x - 2
2y = -x - 2 - 2
2y = -x - 4
y = -½x - 2
Option A
Number 3
For perpendicularity... m1 × m2 = -1
y = 4/3x - 5
y = mx + c
m1 = 4/3
m2 = -1/m1
m2 = -1/(4/3)
m2 = -3/4
(3, -1) = (x1, y1)
y - y1 = m2(x - x1)
y - (-1) = -¾(x - 3)
y + 1 = -¾(x - 3)
4(y + 1) = -3(x - 3)
4y + 4 = -3x + 9
4y = -3x + 9 - 4
4y = -3x + 5
y = -¾x + 5/4
Option A
Number 4
For perpendicularity... m1 × m2 = -1
y = -5x + 5
y = mx + c
m1 = -5
m2 = -1/m1
m2 = -1/-5
m2 = ⅕
(5, 4) = (x1, y1)
y - y1 = m(x - x1)
y - 4 = ⅕(x - 5)
5(y - 4) = x - 5
5y - 20 = x - 5
5y = x - 5 + 20
5y = x + 15
y = ⅕x + 15/5
y = ⅕x + 3
Option C