CC.6

Rate of change of a linear function: graphs

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CC.6Rate of change of a linear function: graphsZPF

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Bryant loves to eat bagels to fuel up for his track meets. He typically buys them fresh from the bakery.

There is a linear relationship between the number of bagels Bryant buys and the total cost.

$10

$11

$12

Number of bagels

Total cost ($)

Describe the rate of change for this relationship.

The total cost

increases

decreases

increases

decreases

0.80

1.00

1.25

5.00

10.00

12.00

0.80

1.00

1.25

5.00

10.00

12.00

per bagel.

ref_doc_title.

Learn with an example

question

Patty 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 Patty's first observation, and the total amount of rainfall, in inches.

Time (hours)

Total amount of rainfall (inches)

Describe the rate of change for this relationship.

The total amount of rainfall

increases

decreases

increases

decreases

of an inch

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

solution

There is a linear relationship between the time, in hours,

since Patty'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

First, identify two points on the line.

Time (hours)

Total amount of rainfall (inches)

(5, 3)

(10, 5)

Find the change in the

-coordinates

from

(

)

and

(

)

This is the change in the total amount of rainfall.

–

Find the change in the

-coordinates.

This is the change in time.

–

Divide to find the rate of change.

of an inch per hour

Notice that the rate of change is

positive.

Also notice that the line on the graph goes up as it goes from left to right. Both observations indicate that as the time since Patty's first observation increases, the amount of rainfall

increases.

This sentence describes the rate of change for this relationship:

The amount of rainfall increases by

of an inch

per hour.

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