Answer
Constant of Variation: $\dfrac{2}{3}$
When $x=-0.5,$ $y=-\dfrac{1}{3}.$
Work Step by Step
The model used for a direct variation is $y=kx.$ Given that $
y=2
\text{ when }
x=3
,$ the value of the constant of variation, $k,$ is
\begin{align*}
y&=kx
\\
2&=k(3)
\\\\
\dfrac{2}{3}&=k
\end{align*}
Hence, the direct variation equation is $
y=\dfrac{2}{3}x
.$ Substituting the given value, $x=-0.5,$ then the value of $y$ is
\begin{align*}\require{cancel}
y&=\dfrac{2}{3}x
\\\\
y&=\dfrac{2}{3}(-0.5)
\\\\
y&=\dfrac{2}{3}\left(-\dfrac{1}{2}\right)
\\\\
y&=\dfrac{\cancel2^1}{3}\left(-\dfrac{1}{\cancel2^1}\right)
\\\\
y&=-\dfrac{1}{3}
\end{align*}
Hence, $
y=-\dfrac{1}{3}
$ when $x=-0.5$.
