# How do you write an inverse variation equations given x = 0.5 when y = 2.5?

Jan 8, 2018

$y = \frac{1.25}{x}$

#### Explanation:

$\text{the initial statement is } y \propto \frac{1}{x}$

$\text{to convert to an equation multiply by k the constant}$
$\text{of variation}$

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

$\text{to find k use the given condition}$

$x = 0.5 \text{ when } y = 2.5$

$y = \frac{k}{x} \Rightarrow k = y x = 2.5 \times 0.5 = 1.25$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{1.25}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$