Suppose y varies inversely with x, how do you write an equation for the inverse variation if y = 8 when x = 1/2?

Jun 2, 2015

Since it is an inverse variation it can be represented as:
 color(red)(y) = color(blue)(k/color(red)(x , where color(blue)(k represents the constant term , $\textcolor{red}{x \mathmr{and} y}$ are the variables.

Values for the variables are:
$y = 8$ and $x = \frac{1}{2}$

substituting these values :
 color(red)(y) = color(blue)(k/color(red)(x
 color(red)(y.x) = color(blue)(k

$\frac{1}{2} . 8 = \textcolor{b l u e}{k}$
we get the constant as $\textcolor{b l u e}{k} = 4$

 color(red)(y) = color(blue)(4/color(red)(x

 color(red)(x.y) = color(blue)(4, represents the inverse variation in which constant is $4$.