rate of change

A rate of change tells you how fast one quantity moves as another changes — like speed (miles per hour) or a price (dollars per pound). It answers “how much does the output shift for each step of the input?”

Between two data points it is computed as the change in the output divided by the change in the input: (change in y) / (change in x). For a straight line this number is constant, and it is exactly the slope. That is why slope and rate of change are two names for the same idea in linear settings.

Honest caveat: only straight lines have a single constant rate of change. For a curve, the rate keeps shifting from point to point, and what we just computed is an average rate of change over the interval — the instantaneous rate is a calculus idea for later.