AB has a midpoint of \(\displaystyle{\left({\left(\frac{{-{2}+{6}}}{{2}}\right)},\frac{{-{2}+{6}}}{{2}}\right)}{)}{)}={\left({2},-{1}\right)}\). The slope of AB is \(\displaystyle\frac{{{y}{2}-{y}{1}}}{{{x}{2}-{x}{1}}}=\frac{{{6}-{\left(-{2}\right)}}}{{{6}-{\left(-{2}\right)}}}=\frac{{2}}{{8}}=\frac{{1}}{{4}}\) so the slope of its perpendicular bisector is -4. Using point slope form of a line, the equation of the perpendicular bisector of AB is:

y-y1=m(x-x1)

y-(-1)=-4(x-2)

y+1=-4x+8

y=-4x+7

y-y1=m(x-x1)

y-(-1)=-4(x-2)

y+1=-4x+8

y=-4x+7