Answer
$k=-\dfrac{2}{3}$
When $x=-3$, the value of $y$ is $2$.
Work Step by Step
Recall:
The formula for direct variation is $y=kx$ where $k$ is the constant of variation.
When $x=-1.5$, the value of $y$ is $1$.
Substitute these values into the equation above to find the value of $k$:
\begin{align*}
y&=kx\\\\
1&=k(-1.5)\\\\
\frac{1}{-1.5}&=\frac{k(-1.5)}{-1.5}\\\\
-\frac{2}{3}&=k
\end{align*}
Thus, the equaton for the given direct variation is $y=-\dfrac{2}{3}x$.
To find the value of $y$ when $x=-3$, substitute $-3$ into the equation to obtain:
\begin{align*}
y&=-\frac{2}{3}x\\\\
y&=-\frac{2}{3} \cdot (-3)\\\\
y&=2
\end{align*}
