Question 816628
M(-5,4), N(1,-2)

Mid point of MN= (-5+1)/2 , (4-2)/2

=(-2,1)

The perpendicular bisector passes through this point and it is perpendicular to the line joining MN

slope of MN

(y2-y1)/(x2-x1)

(-2-4)/(1-(-5)
-6/6
=-1

slope of perpendicular bisector is +1

The line has slope of 1 and passes through (-2,1)

y-y1=m(x-x1)

(y-1)=1(x-(-2))

y-1=x+2

y=x+3