# How do you find the constant of variation K for the inverse variation and write the inverse variation equation given x= 1/2 y= 14?

Nov 20, 2017

$y = \frac{7}{x}$

#### Explanation:

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

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

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

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

$x = \frac{1}{2} \text{ when } y = 14$

$t = \frac{k}{x} \Rightarrow k = y x = 14 \times \frac{1}{2} = 7$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{7}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$