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All courses Math Foundations · MF.GR.5 44 of 60
Interpret rate of change informally as how much one quantity changes for each change in another.

Read rate of change from a simple table

Problem
Look at the table. Which rate statement describes how y changes for each 1-unit increase in x?
x–y Table: x and y with 4 rows. Open full size
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Hint

Look at two consecutive rows, such as when x goes from 0 to 1, and subtract the y-values to find how much y changed.

Rate of change tells how much y changes each time x increases by 1.

Solution walkthrough

01

Compare the y-values from one row to the next

\[5~→~8~→~11~→~14\]

As x goes up by 1 each time, look at how much y changes from row to row.

02

Find the constant difference

\[\begin{aligned} 8~-~5~=~3, \\ 11~-~8~=~3, \\ 14~-~11~=~3 \end{aligned}\]

The y-values increase by 3 each time x increases by 1.

03

Write the rate statement

\[y~\text{increases}~\text{by}~3~\text{for}~\text{each}~1-\text{unit}~\text{increase}~\text{in}~x\]

That sentence states the rate of change in words using the table.

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Another way

  1. You can compare any two consecutive rows. If the y-difference is always 3 when the x-difference is 1, then the rate statement is the same throughout the table.

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Common mistake

A common mistake is looking at the y-values themselves instead of the change in y. The rate of change comes from the difference between rows.