If we set β = f(1), then for any real number x, we have f(x) = βx and the graph of this function is the straight line in the plane passing through the origin with slope β.

How about not plotting a linear function? Let's just plot x vs. t. Again, technically this should be t vs x since t is the dependent variable---but damn the rules!

Graphs that are not drawn to scale mislead the reader. This post shows another example of a graph where the visual representation of the numbers is not proportional to the numbers themselves.