Answer
Slope: $\frac{3}{2}$
$y$-intercept: $3$
Work Step by Step
We first must put the equation $2y-6=3x$ into slope-intercept form.
To do this, first we add $6$ to both sides of the equation: $2y=3x+6$
Then we divide both sides of the equation by $2$: $y=\frac{3}{2}x+3$
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 pick out the slope and the $y$-intercept from the equation $y=\frac{3}{2}x+3$.
Since $\frac{3}{2}$ takes the place of $m$ in the equation, it is the slope.
Since $3$ takes the place of $b$ in the equation, it is the $y$-intercept.
