a line through (-2,7) and (-8,-3) has slope =

(7--3)/(-2--8) = 10/6 = 5/3

perpendicular lines have the negative inverse slope = -3/5

change the sign and flip the fraction upside down

y=mx + b

y=-3x/5 + b

plug in the midpoint to calculate b, the midpoint is the average of the coordinates: (-5, 2)

average x coordinate = (-2-8)/2 = -10/2 =-5

average y coordinate = (7-3)/2 = 4/2 = 2

2 =-3(-5)/5 + b

b = 2-3 =-1

the perpendicular line has the equation

y=-3x/5 -1

or

5y =-3x -5

or

3x +5y +-5

It may help to plot the points and and graph the lines

even a rough sketch can help.