# If x varies inversely as y, and x = 13 when y = 9, how do you find x when y = 0, 3, 6, 12, 15, 18?

Jul 9, 2015

$x = \frac{117}{y}$

#### Explanation:

x varies inversely as y $\setminus \Leftrightarrow x \setminus \propto \frac{1}{y} , y \setminus \ne 0$
$x = f \left(y\right) = k \cdot \frac{1}{y}$

$13 = f \left(9\right) = \frac{k}{9}$

$13 \cdot 9 = k$

$x \left(3\right) = \frac{13 \cdot 9}{3} = 39$

$x \left(6\right) = \frac{13 \cdot 9}{6} = \frac{39}{2}$

$x \left(12\right) = \frac{13 \cdot 9}{12} = \frac{39}{4}$

$x \left(15\right) = \frac{13 \cdot 9}{15} = \frac{39}{5}$

$x \left(18\right) = \frac{13 \cdot 9}{18} = \frac{13}{2}$