The Area Under a Rate Graph Is the Amount

You'll learnto read an accumulated amount off the area under a rate graph, to get its units by canceling the two axes, to tell a net change apart from a total area on one picture, and to place the largest amount where the rate crosses zero rather than where the rate is biggest.

A rate times an elapsed time is an amount, and on a graph of the rate that product is an area. Everything in this unit grows out of that one sentence, and everything expensive in it is in the word area, because half of an area can be negative. The same shaded picture answers "how much did the tank change" and "how much water moved" with two different numbers, and nothing in the geometry tells you which one was asked for. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · A HEIGHT IS A RATE, AN AREA IS AN AMOUNT · v2

height = a rate · width = a time · area = the amount

Before you start

What you're looking at

Two panels on the same horizontal scale. Above is a flow rate in liters per minute; below is how much has been collected by each moment, so the lower height is the shading standing to its left.

The question

If the height is a rate and the width is a time, what is the area — and what happens to it once the rate goes below the axis?

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