Question

Consider the line y = 3/8x + 3

Find the equation of the line that is perpendicular to this line and passes through the point (-8,-4).
Find the equation of the line that is parallel to this line and passes through the point (-8, – 4).

Answer 1

Perpendicular line y = (- 8/3)x - 76/3.

Parallel line y = (3/8)x - 1

Explanation:

y = 3/8

x + 3

1) Perpendicular line has negative reciprocal slope.

m = - 8/3

y = (- 8/3)x + b

Point (-8, - 4)

- 4 = (- 8/3)*(-8) + b

-4 - 64/3 = b

b = - 76/3

y = (- 8/3)x - 76/3

2) Parallel line has the same slope.

m = 3/8

y = (3/8)x + b

Point (-8, -4)

- 4 = (3/8)*(- 8) + b

- 4 + 3 = b

b = - 1

y = (3/8)x - 1