Answer
The value of y is \[-6\].
Work Step by Step
Use the formula, \[m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\], where m is slope of the line passing through points \[\left( {{x}_{1}},{{y}_{1}} \right)\]and \[\left( {{x}_{2}},{{y}_{2}} \right)\].
Take \[\left( {{x}_{1}},{{y}_{1}} \right)=\left( -2,y \right)\] and \[\left( {{x}_{2}},{{y}_{2}} \right)=\left( 4,-4 \right)\], \[m=\frac{1}{3}\].
Slope of the line is:
\[m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]
\[\begin{align}
& m=\frac{-4-y}{4-\left( -2 \right)} \\
& \frac{1}{3}=\frac{-4-y}{4+2} \\
& \frac{1}{3}=\frac{-4-y}{6} \\
& 1=\frac{-4-y}{2}
\end{align}\]
Apply cross-products principle:
\[\begin{align}
& 2=-4-y \\
& y=-4-2 \\
& y=-6 \\
\end{align}\]
Thus, the value of y is \[-6\].
