Math 1 · Unit 2 · Lesson 6 · part 2 of 5

The idea: how much, for each step

Lesson 5 said steeper means faster.

The idea: how much, for each step

Lesson 5 said steeper means faster. This lesson puts a number on it. Pick two points on a function. Between them, the output changed by some amount and the input changed by some amount. The average rate of change is how much the output changed for each step of the input, over that stretch:

average rate of change = change in the outputchange in the input

Say it plainly: how much it went up or down, for each step to the right. It is a fraction, and we keep the fraction reasoning from Unit 1: the top (the numerator) is the change in the output, the bottom (the denominator) is the change in the input. Divide, and you get the change per one step.

The stretch of inputs you picked, from one value to another, is called the interval. Say which interval you used every time, because a curve can have a different rate on a different interval.

Three moves, every time. Pick two points. Subtract the outputs (second minus first) for the top. Subtract the inputs (second minus first, same order) for the bottom. Divide. Then read it back into the story: about 2 inches per week, 3 blocks per minute, 15 dollars per ticket.

The sign tells the directionA positive rate means the output went up as you moved right: the graph is climbing on that interval. A negative rate means it went down: falling. A rate of 0 means flat. The size tells how steep: 4 per step is steeper than 1 per step. Next unit this number gets its real name, slope, and pairs up with the equation of a line. For now, call it what it is: the average rate of change.

Where to go next

Next: Three ways to find it: a table, a graph, a ruleA plant's height in inches, week by week. All the partsAverage Rate of Change: How Fast It Is Changing