#### Answer

$z=\frac{1}{2}xy$

#### Work Step by Step

If $z$ is directly proportional to the product of $x$ and $y$ and if $z$ is 10 when $x$ is 4 and $y$ is 5, then $x$, $y$, and $z$ are related by the equation ___$z =\frac{1}{2}xy$___.
We know this because $z$ is jointly proportionaI to $x$ and $y$. So the general equation must be: $z=kxy$. To solve for $k$, we substitute the given values:
$10=k*4*5$
$10=20k$
$k=\frac{1}{2}$