# Suppose that y varies inversely with x. Write a function that models the inverse function. x = 1 when y = 12?

## y=1/12 x y=12/x y=1/12x y=12x

Mar 21, 2017

$y = \frac{12}{x}$

#### Explanation:

The statement is expressed as $y \propto \frac{1}{x}$

To convert to an equation introduce k, the constant of variation.

$\Rightarrow y = k \times \frac{1}{x} = \frac{k}{x}$

To find k use the condition that x = 1 when y = 12

$y = \frac{k}{x} \Rightarrow k = x y = 1 \times 12 = 12$

$\Rightarrow y = \frac{12}{x} \text{ is the function}$