What happens when the graph of a relation appears linear, but there is no common difference between adjacent x-values and no common difference between adjacent y-values?

In the graph shown, four points are plotted, but there is no common distance between any pair of points, and thus there is no common difference for the x-values or the y-values. 

Still, the relation represented by the graph above is clearly linear, so there must be another way to confirm.

Linear relations are proportional. By comparing the ratios of the x-values and y-values of any two sets of ordered pairs belonging to the relation, you will find they are the same.

Using the red arrows on the graph as a guide, notice that to get from the point (-3, 6) to the point (-1, 5), there is a vertical drop of 1 unit and a horizontal slide of 2 units. This and other similar relationships are summarized in the table below.

When reduced, the ratio is 1:2 for each set of ordered pairs, so this relation is linear.