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Slope Is the Rate of Change

A linear function changes by the same amount for every unit step, so any two points on it give the same difference quotient -- the slope -- and a graph through the origin is a direct proportion whose slope is the unit rate. Shifting a line or reading a runner's speed off a graph uses that constant rate; a graph made of straight pieces, like an area that grows and then shrinks as a point moves, has its own constant slope on each piece and changes rate only where the pieces join.

Builds on: Signed Position and DistanceProportion and Proportional DivisionA Function Sends Each Input to Exactly One Output

Progression (4)