Question

Consider the line y = - 4x +8.

Find the equation of the line that is perpendicular to this line and passes through the point (-6, 4).
Find the equation of the line that is parallel to this line and passes through the point (-6, 4).

Answer 1

The equation for the parallel line is: y = -4x - 20

The equation for the perpendicular line is: y = 1/4x + 11/2

Explanation:

The given point is: (-6, 4)

The given equation is:

y = -4x + 8, note the slope m = -4.

A parallel line has the same slope. Use the point slope and substitute:

y - y1 = m(x - x1)

y - 4 = -4(x - (-6))

y - 4 = -4(x + 6)

y - 4 = -4x - 24

y = -4x - 20

Proof - find f(x) when x = -6:

f(x) = -4x - 20

f(-6) = -4(-6) - 20

f(-6) = 24 - 20 = 4, so the point is (-6, 4)

A perpendicular line has a slope that is negative and inverted so m = 1/4.

y - y1 = m(x - x1)

y - 4 = 1/4(x - (-6))

y - 4 = 1/4(x + 6)

y - 4 = 1/4x + 6/4

y - 4 = 1/4x + 3/2

y = 1/4x + 3/2 + 4

y = 1/4x + 3/2 + 8/2

y = 1/4x + 11/2

Proof - find f(x) when x = -6:

f(x) = 1/4x + 11/2

f(-6) = 1/4(-6) + 11/2

= -6/4 + 11/2

= -3/2 + 11/2

= 8/2 = 4, giving the point (-6, 4)