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.