Answer
The value of y is $y=-6$.
Work Step by Step
Consider a line passing through the points $\left( -2,y \right)$ and $\left( 4,-4 \right)$. The slope of the line is $m=\frac{1}{3}$.
The slope of a straight line that passes through the points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is as follows:
$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Substitute $m=\frac{1}{3}$, $\left( {{x}_{1}},{{y}_{1}} \right)=\left( -2,y \right)$, and $\left( {{x}_{2}},{{y}_{2}} \right)=\left( 4,-4 \right)$ and get the value of y as follows:
$\begin{align}
& \frac{1}{3}=\frac{\left( -4 \right)-y}{4-\left( -2 \right)} \\
& \frac{1}{3}=\frac{-4-y}{4+2} \\
& -4-y=\frac{1}{3}\times 6 \\
& -4-y=2
\end{align}$
Simplify further:
$\begin{align}
& -y=2+4 \\
& -y=6 \\
& y=-6
\end{align}$
Therefore, the value of y is $-6$ so that the slope of the line passing through points $\left( -2,y \right)$ and $\left( 4,-4 \right)$ is $m=\frac{1}{3}$.
