# Suppose that a y varies inversely with x, and y=6 when x=8. What is an equation for the inverse variation?

May 12, 2018

#### Answer:

$y = \frac{1}{x} + \frac{47}{8}$

#### Explanation:

$y$ varies inversely as $x$, therefore
$y = \frac{1}{x} + c$, where $c$ is an unknown constant

substitute $y$ for 6 and $x$ for 8:
$6 = \frac{1}{8} + c$
$6 - \frac{1}{8} = \frac{1}{8} + c - \frac{1}{8}$
$\frac{\left(6 \times 8\right) - 1}{8} = c$
$\frac{48 - 1}{8} = c$
$\frac{47}{8} = c$

replace $c$ with $\frac{47}{8}$ in $y = \frac{1}{x} + c$
answer: $y = \frac{1}{x} + \frac{47}{8}$