# Why is the meaning of “linear” different in school and college use?

Is the map $$y=2x+3$$ linear?

"Of course it is." -- a high school teacher will answer.

"Nope; it's affine, but not linear." -- a college student will contradict.

This difference terminology that basic ought to have historical roots. Could you point toward them?

• – Michael E2 Jun 5 '19 at 23:08
• This question is more suitable for Math Ed SE. The original "linear" refers to the graph being a line. In more advanced fields (linear algebra, functional analysis) it makes sense to make the finer linear/affine distinction, but there is little point to it in school/freshman math. – Conifold Jun 6 '19 at 1:46

Yes, it has historic roots. The term "linear" is much older than "affine" and the function $$ax+b$$ is "linear" because its graph is a straight line. With the invention of linear algebra, the meaning of the world linear changed. But educators, especially on the lower level are very conservative, and also reluctant to introduce extra Greek terms (which on their opinion intimidate students). So the terminology in lower levels of mathematical education lags behind the development of mathematics.