If y varies inversely with x, and y= 6 when x= 18, how do you find y when x= 8?

Jul 9, 2016

$y = 13.5$

Explanation:

y prop 1/x or y = k*1/x or x*y=k; y=6 ; x=18 :. 6*18=k or k=108 k= constant of variation. So the inverse variation equation is $x \cdot y = 108$
Now $x = 8 \therefore 8 \cdot y = 108 \mathmr{and} y = \frac{108}{8} = 13.5$[Ans]

Jul 9, 2016

$y = \frac{13}{5}$

Explanation:

Inverse variations look like this: $y = \frac{k}{x}$

We need to make our own inverse variation given $y = 6$ and $x = 18$. We can plug this into the standard inverse variation with variables.

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

$6 = \frac{k}{18}$

$108 = k$

We've determined that $k = 108$. Now we have what it takes to create an inverse variation. This is our final equation:

$y = \frac{108}{x}$

We still need to find what $y$ equals when $x$ is $8$. Let's plug in $8$ for $x$.

$y = \frac{108}{x}$

$y = \frac{108}{8}$

$y = 13.5$