Question

Variation Suppose that z is inversely proportional to y, and that $z=12$ when $y=16$. Write an equation that expresses z in terms of y.

Short answer

The equation of the inverse variation is $z=\frac{192}{y}$.

Step-by-step solution

Step 1. Write the given information.

The value of z varies inversely as y.

The value of z is 12.

The value of y is 16.

Step 2. Write the direct relationship.

The equation that expresses the inverse relation between z and y is given as,

$z=\frac{k}{y}\mathrm{...}\left(1\right)$

Here, k is the constant of proportionality.

Substitute 16 for y and 12 for z in equation (1).

$\begin{array}{c}12=\frac{k}{16}\\ k=16\cdot 12\\ =192\end{array}$

Step 3. Find variation.

Substitute 192 for k in equation (1).

$z=\frac{192}{y}$

Thus, the equation for variation is $z=\frac{192}{y}$.