The equation of AB is y = 1/2x + 4

We need to find the mid-point of AB....this is :

[  (2 + 6)/2, (5 + 7) /2)  =   ( 8 / 2, 12 / 2)   = (4, 6)   

The perpendicular bisector will go through this point...and it will have a slope of -2

So .....its equation is

y  =  -2 ( x - 4)   + 6  

y = -2x + 8 + 6

y = -2x + 14

The equation is

y  = m(x - h)  + k

Where m is the slope of the perpendicular bisector.....and ( h, k)  = ( 4, 6)  which is a point on the perpedicular bisector....in this case, it's the midpoint of AB