#### Answer

$xy=250$
When $x=10$, the value of $y$ is $25$.
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 $x=2.5$ when $y=100$, substitute these into the formula $xy=k$ to obtain:
\begin{align*}
xy&=k\\\\
2.5(100)&=k\\\\
250&=k\end{align*}
Therefore, the equation that models the inverse variation is $xy=250$.
To find the value of $y$ when $x=10$, substitute $10$ to $x$ in the equation above to obtain:
\begin{align*}
xy&=250\\\\
10(y)&=250\\\\
y&=\frac{250}{10}\\\\
y&=25
\end{align*}
Use a graphing utility to obtain the graph above.