If line segment ab is defined by the endpoints a(4,2) and b(8,6) , write an equation of a line that is the perpendicualr bisector line segment ab

Slope of line ab  = 6-2 / 8-4  = 4/4 = 1
So the slope of the perpendicular line is -1/1  = -1
This line passes through the midpoint of ab
The midpoint of ab  =  ( 8+4 / 2 , 2+6 / 2) =  (6, 4)
Finding the equation of the perpendicular line:-
y - y1 = -1(x - x1)  where x1 = 6 and y1 = 4:-
y - 6 = -1(x - 4)
y = -x + 10 is the answer