# F(x) varies inversely with x and f(x) = –10 when x = 20. What is the inverse variation equation?

Jan 5, 2017

$F \left(x\right) = - \frac{200}{x}$

#### Explanation:

$F \left(x\right) \text{ }$varies inversely with $x$

$\implies F \left(x\right) \text{ "alpha" } \frac{1}{x}$

ie.$\text{ " F(x)=k/x" }$for some constant $k$

use the given data to find $k$

$- 10 = \frac{k}{20}$

$\implies k = - 200$

$\therefore F \left(x\right) = - \frac{200}{x}$