S2 · Functions · FUNC.LINEAR
Linear functions
A linear function has the form . m is the slope and b the y-intercept.
Intuition
Understand first, compress later.
m describes how much y changes when x increases by 1. b tells you where the line starts at .
Switch representations
Linear functionf(x) = x
graph of fΔx (run)Δy (rise)y-intercept
Formal view
For two points, . Then b can be determined from .
Why does it work?
A constant rate of change means equal changes in x always produce equal changes in y — geometrically, a straight line.