# How do you write inverse variation equation given x = 8, y = 24?

Oct 29, 2015

$y = \frac{192}{x}$

#### Explanation:

An inverse equation, by definition, is $y = \frac{k}{x}$, which translates in English to "y is inversely proportional to x". $k$ is the constant of the function.

To determine the inverse equation for your problem, simply plug in the values given into the basic equation of an inverse equation. Solve for $k$. Then rewrite the inverse equation with the value for $k$.

First, plug in your values. Doing so gets you:

$24 = \frac{k}{8}$

If we multiply both sides by $8$ since we are trying to solve for $k$, we get:

$192 = k$ or $k = 192$, by the reflexive property of equations.

Now, plug in the value of $k$ into the basic equation. Doing so results in:

$y = \frac{192}{x}$.