# If y varies inversely with x, and y = 5 when x = 7, what is the value of y when x = 4?

Jul 7, 2016

$y = 8 \frac{3}{4}$ when $x = 4$

#### Explanation:

An inverse variation: $y = \frac{k}{x}$

We are given $y$ and $x$. We need to solve for $k$ so we can find $y$ when $x$ equals $4$.

$5 = \frac{k}{7}$

$\frac{7}{1} \cdot 5 = \frac{k}{\cancel{7}} \cdot \frac{\cancel{7}}{1}$

$35 = k$

We found what $k$ is, so know we can make our inverse variation equation.

$y = \frac{35}{x}$

Now let's plug in $4$ for $x$ to find $y$.

$y = \frac{35}{4}$

$y = 8 \frac{3}{4}$