The Geometry of y = mx + b

by Henri Picciotto

Most math students in the US never see a formal proof that the formula y = mx + b has a graph that is a straight line, and conversely that a non-vertical line has an equation of the form y = mx + b. This is probably due to the fact that similar triangles are studied later than linear functions, and since the curriculum values breadth over depth, one doesn't usually take the time to come back to this topic.

This worksheet guides the reader through such a proof.

And this one goes on to prove a related result for function diagrams.

Prerequisite:Familiarity with both linear functions and similar triangles.