Making Graphs

Most of the graphing you will be doing will be graphs of a straight line. We will often work equations into a linear relationship between two variables, such that the slope or the intercept of the resultant line is equal to a certain quantity. The following are some tips and suggestions on how to make good linear graphs:

Circle your data points. This is just good housekeeping. A dot with a circle is much less likely to be mistaken for a stray mark.

Scale your axis properly. Since you will generally be reading information from your graphs, it is important that the error in drawing them be small. To illustrate, suppose you had to make a mark at 2.5 meters on your graph. If your scale is 10 meters per division, the most accurate mark you could make would be at 5 meters (I assume you can estimate the 1/2 mark much better than the 1/4 mark). This is a fairly inaccurate measurement - 5m compared to 2.5m. But if your scale were 1 meter per division, you could mark 2.5 meters to an extremely high degree of accuracy.

Don't connect the dots. When you graph what is to be considered a straight line, remember that each data point will contain some amount of error. Therefore, it is inconsistent to assume that each point is on the line. A more accurate assumption is that the point is near the line. When you draw your line, use a straight edge and draw it through the middle of your data points. In doing so, you are making the assumption that the line is the theoretically correct locus of points.

Use large distances to calculate your slopes. Again, this has to do with accuracy in measurement. One millimeter is small compared to 10 centimeters (1%), but large compared to one centimeter (10%). Therefore, if you are measuring the slope of a 10cm by 10cm graph use larger Δx and Δy values, on the order of 10cm, instead of smaller values like 1cm. That way, the error you unavoidably introduce in your measurement will be a tiny fraction of the quantity you are measuring.

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Examples of Good and Bad Graphs

These three graphs were made from the same data to illustrate the varying ways to make a graph. The first graph is the correct graph, and the others are bad variations of it.

Notice that the data points are spread across the entire span of both axis. This scaling makes the most of the space provided, and gives you a fighting chance at placing the data points accurately.
On the other hand, I can barley see the separation of the data points in the second graph. If it weren't done by a computer, I would be extremely skeptical about the accuracy of the placement of the data. In short, your graphs should not look like this.
It is probably a good rule of thumb to never do this on a graph. 99.9% of the time, you will be graphing what everyone hopes is a straight line. So when you draw that line, draw what you should get - not what you actually got. Remember, it is expected that your data stray from the theory a bit. Therefore, it is expected that your data points stray from the line a bit.