As the midpoint is a point on the perpendicular line, we can solve by eliminating the other equations, like this:
Check if the point (-1,-2) is on the line y=-4x-4:
-4(-1)-4=0 is differente from -2.
-4(-1)-6=-2, so (-1,-2) is on the line y=-4x-6.
We check also for the other equation like this:
Third equation: (-1)-4 = -5 not equal to -2.
Fourth equation: (-1)-6=-7 not equal to -2.
So the correct answer is the line y=-4x-6
