Assume y varies inversely as x, how do you write the equation given y=-4 when x=16?

Mar 24, 2017

$y = - \frac{64}{x}$

Explanation:

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

"inverse means " 1/("variable")

To convert into 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 y = - 4 when x = 16

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

$\Rightarrow k = - 4 \times 16 = - 64$

$\text{Equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = - \frac{64}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$