Answer
$3x+2y+2=0$
Refer to the graph below.
Work Step by Step
Using $
y-y_1=m(x-x_1)
$ or the Point-Slope Form, with $m=-\dfrac{3}{2}$ and passing through the point $(0,-1),$ then
\begin{align*}
y-(-1)&=-\dfrac{3}{2}(x-0)
\\\\
y+1&=-\dfrac{3}{2}x
\\\\
2(y+1)&=\left(-\dfrac{3}{2}x\right)2
\\\\
2(y)+2(1)&=-3x(1)
\\
2y+2&=-3x
\\
3x+2y+2&=0
.\end{align*}
To graph the line, interpret the slope, $m,$ as $m=\dfrac{rise}{run}.$ With $m=-\dfrac{3}{2}=\dfrac{-3}{2},$ then $rise=-3$ and $run=2.$ Starting at the given point $(0,-1),$ move $3$ units down (since $rise$ is negative) and then move $2$ units to the right. This gives the point $(2,-4)$. Connecting these points gives the graph of the line (see above).
