#### Answer

The condition that y varies directly as x and directly as z can be modeled by the equation $y\ =\ k\ \times \ x\ \times \ z$.

#### Work Step by Step

The variable y varies jointly as x and z 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 directly as z means $y\ \propto \ z$ , which implies that when the variable z increases, y also increases or when z decreases, y also decreases.
Thus, we have
$y\ \propto \ x\ \times \ z$
Use the constant of proportionality k, to get:
$y\ =\ k\ \times \ x\ \times \ z$
The variable y varies jointly as x and z can be written as $y\ =\ k\ \times \ x\ \times \ z$ , where k is called the constant of variation or constant of proportionality.