# If y varies inversely as x, and y=10 as x=7, how do you find y for the x-value of 10?

Jun 3, 2015

Inverse variation can be represented as:
$y = \frac{k}{x}$
$k = y . x$

where color(green)(k is the constant

$x = 7 \mathmr{and} y = 10$
so ,
 color(green)(k = 7 xx 10 = 70

Now, we have the value of $\textcolor{g r e e n}{k}$ and $x = 10$ , substituting these in the variation to find color(red)(y
$k = \textcolor{red}{y} . x$

$\textcolor{red}{y} = \frac{k}{x}$

 color(red)(y = 70/10 = 7

on observing the values

• when $x = 7 , \textcolor{red}{y} = 10$ , and
• when $x = 10 , \textcolor{red}{y} = 3$

as the value of $x$ decreases $y$ increases and vice verse as they vary inversely.