# If y varies inversely as x, and y=7 when x=6, what is y when x=3?

Jul 14, 2016

$y = 14$

#### Explanation:

$y \propto \frac{1}{x} \implies y = \frac{k}{x}$ where k is a constant of proportionality.

${y}_{1} = 7 , {x}_{1} = 6$
y_2 = ?, x_2 = 3

$\frac{{y}_{2}}{{y}_{1}} = \frac{\frac{k}{x} _ 2}{\frac{k}{x} _ 1} = \frac{k}{x} _ 2 \cdot {x}_{1} / k = {x}_{1} / {x}_{2}$

$\therefore {y}_{2} = {y}_{1} \cdot {x}_{1} / {x}_{2}$

${y}_{2} = 7 \cdot \frac{6}{3} = 7 \cdot 2 = 14$