If you are given a linear equation and you are trying to find a line perpendicular to that line, you do the negative-reciprocal to your slope. What this means is you flip your slope into a fraction and multiply it by -1. So our slope is -4, so the negative reciprocal is [tex] \frac{1}{4} [/tex].
Given our slope is 1/4, we can solve for the line by substituting our given points into point-slope form. So
-6 = (1/4)*4 + b
-6 = 1 + b
-7 = b
So our equation is:
y = (1/4)x -7
So our answer is C
Hopes this helps!
