#### Answer

The slope of a line that is parallel to the graph of the equation is $-\frac{2}{3}$.

#### Work Step by Step

We are given
$3y+2x=7$
$\rightarrow 3y=-2x+7$
$\rightarrow y=-\frac{2}{3}x+\frac{7}{3}$
Nonvertical lines are parallel if they have the same slope and different y-intercepts.
Write an equation in slope-intercept form of the line where m represents the slope:
$y=mx+b$
$y=-\frac{2}{3}x+\frac{7}{3}$
Therefore, the slope of a line that is parallel to the graph of the equation is $-\frac{2}{3}$