Answer
Our function that models the relationship is:
$z = 10xy$
$z = 360$ when $x = 4$ and $y = 9$.
Work Step by Step
The formula to describe a number $z$ that varies directly with $x$ and $y$ is:
$z = kxy$, where $k$ is the constant of variation.
Plug in the values given so we can find $k$:
$60 = k(2)(3)$
Simplify:
$60 = 6k$
Divide each side of the equation by $6$ to solve for $k$:
$k = 10$
Therefore, our function that models the relationship is:
$z = 10xy$
We are asked to find $z$ when $x$ is $4$ and $y$ is $9$:
$z = (10)(4)(9)$
Multiply:
$z = 360$
