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

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.

Describe the rate of change for this relationship.

The total amount of rainfall by per hour.

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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.

Describe the rate of change for this relationship.

The total amount of money Rebecca makes by 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.

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.

Looking for more? Try these:

Lesson: Slope

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Teacher tools

Work it out

Not feeling ready yet? These can help:

MM.7Complete a table from a graph

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

L.5Unit rates

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