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# Inverse Variation Models

## Identify and solve y=k/x form equations

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Boyle's Law
Teacher Contributed

## Real World Applications – Algebra I

Boyle’s Law

### Student Exploration

Boyle’s Law states that the pressure and volume of a gas are inversely proportional. Looking at the picture on Wikipedia, we can see this relationship.

http://en.wikipedia.org/wiki/File:Boyles_Law_animated.gif What does this mean? How does this represent an inversely proportional relationship?

A bicycle pump is a great example that shoes Boyle’s Law. When you push down on the pump, the volume inside the bike pump decreases, and the pressure of the air increases so that it’s pushed into the tire.

If the volume inside of a bicycle pump is 8.2 cubic inches, and the pressure is 19.1 psi, we can find the equation that represents this situation. We know from Boyle’s law that the volume, “y\begin{align*}y\end{align*}” equals the constant divided by the pressure in psi. Our equation is

y=156.62x\begin{align*}y=\frac{156.62}{x}\end{align*}

If we were to substitute any value for the pressure, the output is also changing. As the pressure increases, the volume decreases.

Now let’s take a look at a graph that demonstrates this relationship.

As you can see above, the graph of the bicycle pump represents an inverse variation relationship. As the input, x\begin{align*}x\end{align*}, or the pressure, increases, the volume, the output, or y\begin{align*}y\end{align*}, decreases.

### Extension Investigation

What other physics-related topics demonstrate inverse variation models? How do you see this in everyday life?

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