Awalking path across a park is represented by the equation y = –4x + 10. a new path will be built perpendicular to this path. the paths will intersect at the point (4, –6). identify the equation that represents the new path.

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 .

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!