## 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.

 Volume (mL) Pressure (Bar) 11.5 2.027 12.8 1.824 14.4 1.621 16.4 1.419 19.2 1.216 23.0 1.013

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

Uses the JSXGraph JavaScript libraries.

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.

 Volume (mL) 1/Pressure (Bar-1) 11.5 0.4935 12.8 0.5483 14.4 0.6168 16.4 0.7049 19.2 0.8224 23.0 0.9869
Uses the JSXGraph JavaScript libraries.