Answer
$k=-\dfrac{4}{3}$
When $x=-0.3,$ $y=\dfrac{2}{5}$.
Work Step by Step
Since $y$ varies directly as $x,$ then the model equation is $y=kx.$ Using the given values, $
y=4 \text{ and }
x=-3
,$ then
\begin{align*}
y&=kx
\\\\
4&=k\left(-3\right)
\\\\
\dfrac{4}{-3}&=k
\\\\
k&=-\dfrac{4}{3}
.\end{align*}
With the value of $k$ above, the variation equation is $y=
-\dfrac{4}{3}
x.$ Substituting $x=-0.3$ in the derived variation equation, then the value of $y$ is
\begin{align*}\require{cancel}
y&=-\dfrac{4}{3}(-0.3)
\\\\
y&=-\dfrac{4}{3}\left(-\dfrac{3}{10}\right)
&\text{ (express $-0.3$ as a fraction)}
\\\\
y&=-\dfrac{\cancel4^2}{3}\left(-\dfrac{3}{\cancel{10}^5}\right)
&\text{ (divide by $2$)}
\\\\
y&=-\dfrac{2}{\cancel3^1}\left(-\dfrac{\cancel3^1}{5}\right)
&\text{ (divide by $3$)}
\\\\
y&=-\dfrac{2}{1}\left(-\dfrac{1}{5}\right)
\\\\
y&=\dfrac{2}{5}
.\end{align*}
