Answer
$\dfrac{21}{8}$
Work Step by Step
Recall:
An inverse variation is represented by the equation $xy=k$, where $k$ is the constant of variation.
As the value of $x$ increases, the value of $y$ decreases.
The equation that models the inverse variation can be determined by finding 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 inverse variation formula $xy=k$.
Since the variation contains the point $\left(3, 7\right)$, substitute these into the formula $xy=k$ to obtain:
\begin{align*}
xy&=k\\\\
3(7)&=k\\\\
21&=k\\\\
\end{align*}
Thus, the equation of the inverse variation is $xy=21$.
To find the value of $y$ when $x=8$, substitute $8$ to $x$ in the equation above to obtain:
\begin{align*}
xy&=21\\\\
8(y)&=21\\\\
\frac{8(y)}{8}&=\frac{21}{8}\\\\
y&=\frac{21}{8}\end{align*}
