The given line segment has a midpoint at (−1, −2). what is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment? y = −4x − 4 y = −4x − 6 y = x – 4 y = x – 6

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

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