How do you write an inverse variation equation given y = 10 when x = 2?

Aug 28, 2017

$y = \frac{20}{x}$

Explanation:

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

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

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

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

$y = 10 \text{ when } x = 2$

$y = \frac{k}{x} \Rightarrow k = y x = 10 \times 2 = 20$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{20}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$