Answer
The linear function whose graph is parallel to $2x-3y=4$ and contains the point $\left( -3,7 \right)$ is $y=\frac{2}{3}x+9$.
Work Step by Step
$2x-3y=4$
Subtract $2x$ from both sides of the above equation
$-3y=-2x+4$
$y=\frac{-2}{-3}x+\frac{4}{-3}$
And,
$y=\frac{2}{3}x-\frac{4}{3}$
The slope of any line parallel to the line given by $2x-3y=4$ is $\frac{2}{3}$.
Hence, the line passing through the point $\left( -3,7 \right)$ is:
$\begin{align}
& y-7=\frac{2}{3}\left( x-\left( -3 \right) \right) \\
& y-7=\frac{2}{3}\left( x+3 \right) \\
& y-7=\frac{2}{3}x+2
\end{align}$
$\begin{align}
& y=\frac{2}{3}x+2+7 \\
& y=\frac{2}{3}x+9 \\
\end{align}$
