W.6

Constant rate of change: graphs

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W.6Constant rate of change: graphsTWW

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Kenny filled his hydroponic garden with water. Each day afterwards, he notices a change in the amount of water in the garden.

There is a linear relationship between the time, in days, since Kenny filled the garden with water and the amount of water in the garden, in cups.

Time (days)

Amount of water (cups)

Describe the rate of change for this relationship.

The amount of water

increases

decreases

increases

decreases

of a cup

per day.

ref_doc_title.

Learn with an example

question

Rebecca is selling lemonade by the glass on the first hot day of summer. She plans to donate her profits to the local animal shelter.

There is a linear relationship between the number of glasses of lemonade Rebecca sells and the total amount of money she makes.

$10

$11

$12

$13

$14

$15

Number of glasses sold

Total amount of money ($)

Describe the rate of change for this relationship.

The total amount of money Rebecca makes

increases

decreases

increases

decreases

0.25

0.50

0.75

1.33

3.00

4.00

0.25

0.50

0.75

1.33

3.00

4.00

per glass she sells.

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 number of glasses of lemonade Rebecca sells,

and the total amount of money she makes,

You can use this formula to calculate the rate of change in dollars per glass:

rate of change

change in total amount of money

change in number of glasses sold

First, identify two points on the line.

$10

$11

$12

$13

$14

$15

Number of glasses sold

Total amount of money ($)

(8, 6)

(4, 3)

Find the change in the

-coordinates

from

(

)

(

)

This is the change in the total amount of money.

–

Find the change in the

-coordinates.

This is the change in the number of glasses of lemonade sold.

glasses of lemonade

–

glasses of lemonade

Divide to find the rate of change.

glasses of lemonade

0.75

per glass of lemonade

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 number of glasses of lemonade sold increases, the total amount of money she makes

increases.

This sentence describes the rate of change for this relationship:

The total amount of money Rebecca makes increases by

0.75

per glass of lemonade she sells.

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