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

k=1

Step-by-step 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

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