Answer
$xy=28$
When $x=10$, the value of $y$ is $\dfrac{14}{5}$.
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 $x=-\frac{4}{15}$ when $y=-105$, substitute these into the formula $xy=k$ to obtain:
\begin{align*} xy&=k\\\\ -\frac{4}{15} \cdot \left(-105\right)&=k\\\\ 28&=k\end{align*} Therefore, the equation that models the inverse variation is $xy=28$. To find the value of $y$ when $x=10$, substitute $10$ to $x$ in the equation above to obtain: \begin{align*} xy&=28\\\\ 10(y)&=28\\\\ y&=\frac{28}{10}\\\\ y&=\frac{14}{5} \end{align*}
Use a graphing utility to obtain the graph above.