# Each pair of points (5.4 , 3) and (2, y) is on the graph of an inverse variation, how do you find the missing value?

Nov 27, 2017

$y = 8.1$

#### Explanation:

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

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

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

$\text{to find k use "(5.4,3)" that is x = 5.4 and y = 3}$

$y = \frac{k}{x} \Rightarrow k = y x = 3 \times 5.4 = 16.2$

$\text{the equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{16.2}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when } x = 2$

$y = \frac{16.2}{2} = 8.1$

$\Rightarrow \left(2 , y\right) = \left(2 , 8.1\right)$