Answer
$y-3=-(x+10)$
Work Step by Step
Recall:
(1) The slope $m$ of a line through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
$$m=\dfrac{y_2-y_1}{x_2-x_1}$$
(2) The equation of a line whose slope is $m$ and passes through the point $(x_1, y_1)$ is:
$$y-y_1=m(x-x_1)$$
Solve for the slope using the formula in (1) above:
\begin{align*}
m&=\dfrac{-5-3}{-2-(-10)}\\\\
&=\dfrac{-8}{-2+10}\\\\
&=\dfrac{-8}{8}\\\\
&=-1
\end{align*}
The line has $m=-1$ and passes through $(-10, 3)$, so use the point-slope formula in (2) above to obtain the equation of the line:
\begin{align*}
y-3&=-1(x-(-10))\\
y-3&=-(x+10)
\end{align*}
