IXL - Rate of change of a linear function: tables (Algebra 1 practice)

Jim and his classmates are excited about the big snowstorm. They are hoping it will snow a lot, so they will have a snow day.

There is a linear relationship between the time it snows, in hours, and the total amount of snow expected on the ground, in inches.

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

Describe the rate of change for this relationship.

The total amount of snow on the ground is expected to by per hour.

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Learn with an example

question

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.

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 hours, since Pam's first observation, and the total amount of rainfall, in inches. You can use this formula to calculate the rate of change in inches per hour:

rate of change

change in total amount of rainfall

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

Subtract to find the change in the total amount of rainfall.

inches

–

inches

of an inch

Subtract to find the change in time.

hours

–

hour

Divide to find the rate of change.

of an inch

hour

of an inch per hour

Notice that the rate of change is

positive.

This corresponds to the relationship in the table: as the time since Pam's first observation increases, the total amount of rainfall

increases.

This sentence describes the rate of change for this relationship:

The total amount of rainfall increases by

of an inch

per hour.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

A.1Add, subtract, multiply, and divide integers

L.5Unit rates

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