How do you find the constant of variation K for the inverse variation and write the inverse variation equation given x=3 y=-8?

Jan 5, 2016

k = - 24 and equation is $y = - \frac{24}{x}$

Explanation:

for y to vary inversely as x this is written $y \propto \frac{1}{x}$

to make an equation we introduce the constant of variation k

equation is then : y = $k \times \frac{1}{x}$ =$\frac{k}{x}$

using the condition that x = 3 when y = - 8

and substituting into the equation gives $- 8 = \frac{k}{3}$

now cross-multiply

$\Rightarrow k = - 24$