## Graphing Example 1

A reason for graphing is to show a possible correlation between two “things”. In other words, a possible cause-and-effect relationship. For this example, I measured different volumes of water using a 100 mL graduated cylinder and then weighed each sample. Since I determined the volume of each water sample (the independent variable), the mass of each sample should change (the dependent variable) by some amount.

A graph of the data might reveal more information about the relationship between the two variables. As you can see, not only does the mass of the water sample increase as the volume of the sample increases, it increases in what appears to be a predictable manner. How can I tell? Press the “Best-Fit Line" button under the data and you’ll see that the data appears to fit a line and is very close to passing through the origin (mass and volume are directly proportional to each other in this example).

 Volume (mL) Mass (g) 10.00 9.787 20.00 20.145 30.00 30.138 40.00 39.855 50.00 49.753 60.00 60.178 70.00 70.159 80.00 80.164 90.00 90.352 100.00 100.286

Data collected 3/22/2012.

Uses the JSXGraph JavaScript libraries.

Pressing the “Best-Fit Line" will also give you values for both the slope and the y-intercept. The slope is the numerical relationship between the y and x axes while the y-intercept is the value when the x variable is zero- the point (0, y-intercept). Keep in mind that you cannot calculate a slope for a relationship that is not linear although you might be able to determine an equation that will allow you to calculate the value of the slope at a certain point for a nonlinear relationship.

Once you have the equation of the best-fit line, you can now use this to predict any value of y (the mass of the water) from a given value of x (the volume of water) at 21 °C. You now have the ability to predict expected results.

Some things to consider when graphing-

1. Unless you have a good reason to do otherwise, the independent data goes on the x-axis while the dependent data goes on the x-axis.
2. A graph must have a title. Something like “Y as a Function of X” or “Y Versus X” is usually a good choice. Just don’t literally use “Y” and “X” in the title!
3. Label the axes and include the units.
4. The scale for each axis must be linear although the x-axis can have a different scale than the y-axis.
5. Unless you have a good reason to not include it, show the origin (0,0) on the graph.
6. The value of the slope needs to have appropriate units and they come from the units for the y-axis divided by the units for the x-axis.
7. Unless you know otherwise, determine the number of digits for the slope by using the division rule for significant figures. My mass data has a minimum of 5 significant figures and the volume data has a minimum of four significant figures. Therefore, I’ve calculated the slope to four significant figures.