Answer
y varies directly as x and inversely as z can be modeled by the equation $y\ =\ k\ \times \ \frac{x}{z}$
Work Step by Step
The variable y varies directly as x means $y\ \propto \ x$ , which implies that when the variable x increases, y also increases or when x decreases, y also decreases.
The variable y varies inversely as z means $y\ \propto \ \frac{1}{z}$ , which implies that when the variable z increases, y decreases or when z decreases, y increases.
Thus, we have
$y\ \propto \ \frac{x}{z}$
Use constant of proportionality k to get:
$y\ =\ k\ \times \ \frac{x}{z}$
The variable y varies directly as x and inversely as z and can be written as $y\ =\ k\ \times \ \frac{x}{z}$ , where k is called the constant of variation or constant of proportionality.
