Answer
$y=\dfrac{56}{3}$
Work Step by Step
Recall:
A direct variation is represented by the equation $y=kx$, where $k$ is the constant of variation.
As the value of $x$ increases, the value of $y$ also increases.
The equation that models the direct variation can be determined by solving the value of $k$:
This can be done by taking any ordered pair $(x, y)$ then substituting the values of $x$ and $y$ into the direct variation formula $y=kx$.
Since the variation contains the point $(3, 7)$, substitute these into the formula $y=kx$ to obtain:
\begin{align*}
y&=kx\\\\
7&=k(3)\\\\
\frac{7}{3}&=k\\\\
\end{align*}
Therefore, the equation that models the direct variation is $y=\frac{7}{3}x$.
To find the value of $y$ when $x=8$, substitute $8$ to $x$ in the equation above to obtain:
\begin{align*}
y&=\frac{7}{3}x\\\\
y&=\frac{7}{3}(8)\\\\
y&=\frac{56}{3}\end{align*}
