Which equation represents a line which is perpendicular to the line y = -4x - 5 A) x + 4y = -32
B) 4x - y = -4
C) 4x + y = 3
D) 4y - x = 4

D) 4y-x=4

Explanation

To find an equation perpendicular to another, the product of the slopes of both equations must equal -1

In y= -4x-5, the slope is -4. To obtain a line perpendicular to this line, -4(x)= -1, where the slope of the new line, x, must equal 1/4.

D must be the answer since it is the only equation that could be manipulated back to y= 1/4x

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

This corresponds correctly with the new slope that we found, therefore correct.

Hope this helped :)