Answer
$y=12$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use $
y=kx
$ and solve for the value of $k$ with the given $x$ and $y$ values. Then use the equation of variation to solve for the value of the unknown variable.
$\bf{\text{Solution Details:}}$
Since $y$ varies directly as $x$, then $y=kx.$ Substituting the given values, $
y=9
$ and $
x=30
,$ then the value of $k$ is
\begin{array}{l}\require{cancel}
9=k(30)
\\\\
\dfrac{9}{30}=k
\\\\
k=\dfrac{3}{10}
.\end{array}
Hence, the equation of variation is given by
\begin{array}{l}\require{cancel}
y=kx
\\\\
y=\dfrac{3}{10}x
.\end{array}
If $x=40,$ then
\begin{array}{l}\require{cancel}
y=\dfrac{3}{10}x
\\\\
y=\dfrac{3}{10}\cdot40
\\\\
y=\dfrac{3}{\cancel{10}}\cdot\cancel{10}(4)
\\\\
y=12
.\end{array}
