Answer
$y=-6$
Work Step by Step
$(-2,y)$ and $(4,-4)$ $;$ $m=\dfrac{1}{3}$
The slope of a line is given by $m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$, where $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are two points through which the line passes.
In this case, let $(x_{1},y_{1})$ be equal to $(-2,y)$ and $(x_{2},y_{2})$ be equal to $(4,-4)$.
Substitute the known values into the formula for the slope of a line and solve for $y$:
$\dfrac{1}{3}=\dfrac{-4-y}{4-(-2)}$
$\dfrac{1}{3}=\dfrac{-4-y}{4+2}$
$\dfrac{1}{3}=\dfrac{-4-y}{6}$
$\dfrac{6}{3}=-4-y$
$2=-4-y$
$y=-4-2$
$y=-6$
