Answer
$y+3=-\dfrac{2}{3}(x+2)$
Work Step by Step
Using the properties of equality, the given linear equation, $
2x+3y=-7
$ is equivalent to
\begin{array}{l}
3y=-2x-7
\\\\
y=-\dfrac{2}{3}x-\dfrac{7}{3}
.\end{array}
Using $y=mx+b$ or the Slope-Intercept form where $m$ is the slope, then the slope of the given line is $
-\dfrac{2}{3}
$. Since parallel lines have the same slope, then the needed linear equation has the same slope and it passes through the given point $(
-2,-3
)$. Using $y-y_1=m(x-x_1)$ or the Point-Slope form where $m$ is the slope and $(x_1,y_1)$ is a point on the line, then the equation of the needed line is
\begin{array}{l}
y-(-3)=-\dfrac{2}{3}(x-(-2))
\\\\
y+3=-\dfrac{2}{3}(x+2)
.\end{array}
