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 − 4y = −4x − 6y = x – 4y = x – 6

we know that
As the midpoint is a point on the perpendicular line, we can solve by eliminating the other equations, like this:

a) Check if the point (-1,-2) is on the line y=-4x-4:

for x=-1
y=-4*(-1)-4--------> y=0
0 is not -2--------> that is not the equation

b) Check if the point (-1,-2) is on the line y = −4x − 6:

for x=-1
y=-4*(-1)-6--------> y=-2
-2 is equal to -2--------> that is  the equation

c) Check if the point (-1,-2) is on the line y = x – 4
for x=-1
y=-(-1)-4--------> y=-5
-5 is not -2--------> that is not the equation

d) Check if the point (-1,-2) is on the line y = x – 6
for x=-1
y=-(-1)-6--------> y=-7
-7 is not -2--------> that is not the equation

therefore

the answer is
y = −4x − 6: