This would be a weird mathematics indeed (there are algebras in which this happens for some nonunit elements, but the real numbers is not one of them). So how do linear functions behave?

In this case, what do we expect? Should this be a linear function? No, our model for the acceleration does not predict that the distance should be proportional to the time.

How to Graph Linear Lines in Microsoft Excel. Data is rarely so uniform and predictable that plotting data points creates a perfectly linear arrangement.

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.

In literature also models are described with quadratic achievement functions. 22, 30, 31, 32 In a quadratic achievement function the (weighted) sum of squared unwanted deviations is minimized ...

Christophe P. Basso has written a new book: Linear Circuit Transfer Functions—An Introduction to Fast Analytical Techniques.