Answer
$$y=\dfrac{2}{3}x+\dfrac{44}{3}$$
Work Step by Step
Recall:
(1) Parallel lines have the same or equal slopes.
(2) Perpendicular lines have slopes whose product is $-1$.
(3) The slope-intercept form of a line's equation is $y=mx+b$ where $m$ is the slope and $b$ is the $y$-intercept.
The line is parallel to $2x-3y=-3$, whose slope is $\frac{2}{3}$.
This means that the slope of the line we are looking for is also $\frac{2}{3}$.
Thus, the tentative equation of the line is:
$$y=\frac{2}{3}x+b$$
Substitute $-7$ to $x$ and $10$ to $y$ to obtain:
\begin{align*}
y&=\frac{2}{3}x+b\\\\
10&=\frac{2}{3}(-7)+b\\\\
10&=\frac{-14}{3}+b\\\\
10+\frac{14}{3}&=b\\\\
\frac{44}{3}&=b
\end{align*}
Thus, the equation of the line is:
$$y=\dfrac{2}{3}x+\dfrac{44}{3}$$
