8: How to scale axes

The preceding steps — choosing x and y, labelling, deciding on minimum and maximum values, and deciding on
interval distance — are steps you need to do for any graph you make, whether you use a computer or
sketch the graph by hand. (Often a computer program will do these steps for you, but sometimes the
program will get them wrong, too).

If you are drawing a graph on paper, there is just one more complication. The graph paper has
predetermined lines, and you need to make your graph fit on the page or half-page or whatever.
You don’t want an effect like the graph on the left!

graph with no units correct graph


I’m sure there’s a formula for doing this, somewhere. But you can also manage by trial and error.
On the graph above, let’s say you need to approximately fill up a space, which has 40 lines for the x-axis.

If you make each line 10 cm, you’ll only use up 15 lines — too few.

If you make each line 2 cm, you’ll need 75 lines — too many. (This is starting to sound like a nursery story…)

If you make each line 5 cm, you’ll need 30 lines — just right (or at least right enough).