# How do you find the constant of variation K for the inverse variation and write the inverse variation equation given x=7 y=5?

Jul 14, 2016

Constant: $k = 35$

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

#### Explanation:

Inverse Variation: $y = \frac{k}{x}$

We are given $x$ and $y$. We can plug these values into the equation above and solve for $k$, the constant in the variation.

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

$35 = k$

We determined that $k$ is the constant. But we are not done yet. We must form a new inverse variation with $k$.

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

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

And that's our newly-written inverse variation.