## Graphing Example 3

Not all data has a linear relationship. Look at the data below that relates pressure and volume to each other. Pressure is **not** directly proportional to volume since the pressure **increases** when the volume **decreases**. And even that’s not linear since it looks like a curve. If you press the “Draw Line" button, you’ll see the first last last data points connected by a line. While I normally cringe when I see students play “connect-the-dots”, I find it can be a useful technique to see if the data really is linear. Connecting the first and last data points will often reveal a nonlinear relationship.

Data taken from Aus-e-Tute, accessed 3/21/2012.

So what do we do next? One technique is to try and find a way to transform the data into a linear relationship. For this data, taking the reciprocal of either the pressure or the volume gives a linear relationship. If you press the “Best-Fit Line" button you’ll see that reciprocal of the pressure is directly proportional to the volume. Another way to word it is that the pressure is inversely proportional to the volume.