Answer
$k=-\dfrac{10}{3}$
When $x=-3$, the value of $y$ is $10$.
Work Step by Step
Recall:
The formula for direct variation is $y=kx$ where $k$ is the constant of variation.
When $x=\frac{3}{2}$, the value of $y$ is $-5$.
Substitute these values into the equation above to find the value of $k$:
\begin{align*}
y&=kx\\\\
-5&=k\left(\frac{3}{2}\right)\\\\
\frac{-5}{\frac{3}{2}}&=\frac{k\left(\frac{3}{2}\right)}{\frac{3}{2}}\\\\
-5 \cdot \frac{2}{3}&=k\\\\
-\frac{10}{3}&=k
\end{align*}
Thus, the equation for the given direct variation is $y=-\dfrac{10}{3}x$.
To find the value of $y$ when $x=-3$, substitute $-3$ into the equation to obtain:
\begin{align*}
y&=-\frac{10}{3}x\\\\
y&=-\frac{10}{3} \cdot (-3)\\\\
y&=10
\end{align*}
