Answer
$x-y=-5$
Work Step by Step
Using $\left( \dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2} \right)$ or the Midpoint Formula, then the midpoint of the line segment joining the points $
(-6,-3) \text{ and } (-8,-1)
$ is
\begin{array}{l}\require{cancel}
\left( \dfrac{-6+(-8)}{2},\dfrac{-3+(-1)}{2} \right)
\\\\
\left( \dfrac{-6-8}{2},\dfrac{-3-1}{2} \right)
\\\\
\left( \dfrac{-14}{2},\dfrac{-4}{2} \right)
\\\\
\left( -7,-2 \right)
.\end{array}
Using $m=\dfrac{y_1-y_2}{x_1-x_2}$ or the Slope Formula, then \begin{array}{l}\require{cancel}
m=\dfrac{-3-(-1)}{-6-(-8)}
\\\\
m=\dfrac{-3+1}{-6+8}
\\\\
m=\dfrac{-2}{2}
\\\\
m=-1
.\end{array}
Taking the negative reciprocal of $m$, then the slope of the perpendicular bisector is $m_p=
1
.$
Using $
(-7,-2)
$ and $m_p=
1
,$ the equation of the perpendicular bisector is
\begin{array}{l}\require{cancel}
y-(-2)=1(x-(-7))
\\\\
y+2=1(x+7)
\\\\
y+2=x+7
\\\\
-x+y=7-2
\\\\
-x+y=5
\\\\
x-y=-5
.\end{array}