Question

The lines kx + 2y = -7 and y = 2x - 5 are perpendicular to each other. Find the value of k.

Answer 1

k=1

Explanation:

1. find the negative reciprocal of the slope of y=2x-5 because that is the slope perpendicular to it.

m=2 ; negative reciprocal is 1/-2

2. isolate y in the first equation

y= kx/-2 + 7/-2

3. the only value for k that would make their slopes the same would be 1

Answer 2

k=1
A perpendicular line will have a slope that is the negative reciprocal of the slope of the original line, so we need m=-1/2
kx+2y=-7
Subtract kx from both sides.
2y=-kx-7
Divide both sides by 2.
y=-1/2x-7/2