Answer
$xy=-\frac{5}{3}$
When $x=10$, the value of $y$ is $-\frac{1}{6}$.
Refer to the graph below.
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 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 inverse variation formula $xy=k$.
Since $x=5$ when $y=-\frac{1}{3}$, substitute these into the formula $xy=k$ to obtain:
\begin{align*}
xy&=k\\\\
5\left(-\frac{1}{3}\right)&=k\\\\
-\frac{5}{3}&=k\end{align*}
Therefore, the equation that models the inverse variation is $xy=-\frac{5}{3}$.
To find the value of $y$ when $x=10$, substitute $10$ to $x$ in the equation above to obtain:
\begin{align*}
xy&=-\frac{5}{3}\\\\
10(y)&=-\frac{5}{3}\\\\
y&=\dfrac{-\frac{5}{3}}{10}\\\\
y&=-\frac{1}{6}
\end{align*}
Use a graphing utility to obtain the graph above.