Answer
The line through A and B has slope $m_{1}=3$.
Any perpendicular line to it has slope $m_{2}=-\displaystyle \frac{1}{3}.$
Work Step by Step
$A=(x_{1},y_{1})=(- 1, \ 2)$
$B=(x_{2},y_{2})=(-2, \ -1)$
The increments in the coordinates are calculated as $\left\{\begin{array}{l}
\Delta x=x_{2}-x_{1}\\
\Delta y=y_{2}-y_{1}
\end{array}\right.$
$\left\{\begin{array}{l}
\Delta x=-2-(-1)=-1\\
\\
\Delta y=-1-2=-3
\end{array}\right.$
Slope of the line that passes through A and B, if the line is nonvertical, ($\Delta x\neq 0)$ is calculated as
$m_{1}=\displaystyle \frac{\Delta y}{\Delta x}=\frac{-3}{-1}=3$,
Any line perpendicular to the nonvertical line that passes through A and B has slope $m_{2}$, such that
$m_{2}=-\displaystyle \frac{1}{m_{1}}=-\frac{1}{3}$
