Answer
Our function that models the relationship is:
$z = \frac{5x}{y}$
$z = \frac{20}{9}$ when $x = 4$ and $y = 9$.
Work Step by Step
The formula to describe a number $z$ that varies directly with $x$ and inversely with $y$ is:
$z = \frac{kx}{y}$, where $k$ is the constant of variation.
Plug in the values given so we can find $k$:
$15 = \frac{k(6)}{2}$
Multiply both sides of the equation by $2$ to eliminate the fraction:
$30 = k(6)$
Divide each side of the equation by $6$ to solve for $k$:
$k = 5$
Therefore, our function that models the relationship is:
$z = \frac{5x}{y}$
We are asked to find $z$ when $x$ is $4$ and $y$ is $9$:
$z = \frac{(5)(4)}{9}$
Multiply:
$z = \frac{20}{9}$
