Answer
$y=-\dfrac{2}{3}x-\dfrac{4}{3}$
Work Step by Step
We know that by the Slope Formula: if $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ are on a line, then the slope is:
$m=\dfrac{y_2-y_1}{x_2-x_1}$.
Hence here:
$m=\dfrac{2-(-2)}{-5-1}=-\dfrac{2}{3}$
We know that if the slope of a line is $m$ and it contains $P_1(x_1,y_1)$, then its equation is:
$y-y_1=m(x-x_1).$
Therefore the equation of the line through the given points is:
$y-2=-\dfrac{2}{3}(x-(-5))\\
y-2=-\dfrac{2}{3}(x+5)\\
y-2=-\dfrac{2}{3}x-\dfrac{10}{3}\\
y=-\dfrac{2}{3}x-\dfrac{4}{3}$
