IXL | Rate of change of a linear function: tables

Pam has been watching her rain gauge during a heavy storm. She made her first observation when she woke up in the morning and has continued to watch throughout the day.

There is a linear relationship between the time, in hours, since Pam's first observation, and the total amount of rainfall, in inches.

Time (hours)	Total amount of rainfall (inches)
1	2 5
2	4 5
3	1 5
4	3 5

Describe the rate of change for this relationship.

The amount of rainfall by per hour.

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Learn with an example

question

Ken is competing in a go-kart race with his friends. The number of laps Ken has left to complete decreases throughout the race.

There is a linear relationship between the time, in minutes, since Ken started the race and the number of laps he has left to complete.

Time (minutes)	Number of laps left
1	7
2	5
3	3
4	1

Describe the rate of change for this relationship.

The number of laps Ken has left by per minute.

key idea

You can use this formula to calculate the rate of change for a linear relationship between two variables,

and

rate of change

change in y

change in x

solution

There is a linear relationship between the time, in minutes, since Ken started the race, and the number of laps he has left. You can use this formula to calculate the rate of change in laps per minute:

rate of change

change in the number of laps left

change in time

Since the relationship is linear, the rate of change is constant. Pick any two rows of the table to calculate the rate of change.

Time (minutes)	Number of laps left
1	7
2	5
3	3
4	1

Subtract to find the change in the number of laps left.

laps

–

laps

–

laps

Subtract to find the change in time.

minutes

–

minute

Divide to find the rate of change.

–

laps

minute

–

laps per minute

Notice that the rate of change is

negative.

This corresponds to the relationship in the table: as the time increases, the number of laps Ken has left

decreases.

This sentence describes the rate of change for this relationship:

The number of laps Ken has left decreases by 2 laps per minute.

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Work it out

Not feeling ready yet? These can help:

B.24Add, subtract, multiply, and divide integers

L.5Unit rates

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