Answer
$-\frac{2}{3}$
Work Step by Step
In order for two non-vertical lines to be parallel, they must have the same slope. Therefore, to find the slope of a line parallel to this one, we must identify the slope of this one.
The slope-intercept form of a linear equation of a non vertical line is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept.
We use this to find the slope of $3y+2x=7$.
First, we must solve for $y$ to put the equation into slope-intercept form.
We subtract $2x$ from each side of the equation: $3y=-2x+7$
We divide by $3$ on both sides of the equation: $y=-\frac{2}{3}x+\frac{7}{3}$
Since $-\frac{2}{3}$ replaces $m$ in the equation, it is the slope we are looking for, and would be the slope of a parallel line.
