CALCUlus help with problem

Question

Find the point on the line -4x+4y-4=0 which is closest to the point (-4,-5).

Answer 1

The point closest to the line lies on the perpendicular

-4x + 4y - 4 = 0

4y = 4x + 4

y = x + 1, the slope of the line is 1. The slope of the perpendicular is -1

y = -x + b

-5 = -(-4) + b

-5 = 4 + b

-9 = b

The equation of the perpendicular is y = -x - 9

Determine the point at which the two lines intersect.

Then use the Distance Formula.