IXL | Interpret the slope and y-intercept of a linear function

Fred hires Trident Electrik Company to install a new light fixture. The electric company will charge an initial fee for the service call. In addition, the total cost of the job includes an installation fee that will depend on how long the job takes.

This situation can be modeled as a linear relationship.

What does the

-intercept

of the line tell you about the situation?

After the initial fee, Fred will pay

per hour.

Including the initial fee, Fred will pay

225

if the job takes 5 hours.

The initial fee for the service call is

After the initial fee, Fred will pay

per hour.

ref_doc_title.

Learn with an example

question

Sandra is making popcorn balls for movie night with her friends. The amount of sugar Sandra needs depends on the amount of popcorn she uses.

This situation can be modeled as a linear relationship.

What does the slope of the line tell you about the situation?

Sandra needs 1 tablespoon of sugar for every cup of popcorn.

Sandra needs 1 tablespoon of sugar for every 3 cups of popcorn.

Sandra needs 2 tablespoons of sugar for every 3 cups of popcorn.

Sandra needs 3 tablespoons of sugar for every 2 cups of popcorn.

key idea

The slope of a line measures the line's steepness and direction. It relates a change in

-values

to a change in

-values.

This is a formula to find the slope of a line using two points:

slope

change in

solution

To determine what the slope tells you about the situation, first find the slope of the line. Start by choosing two points on the line, such as

(

)

and

(

)

Now, calculate the slope.

slope

change in

–

The slope of the line relates a change in the amount of sugar Sandra needs to a change in the amount of popcorn she uses. So, the slope

tells you that the amount of sugar Sandra needs increases by 2 tablespoons for every 3 cups of popcorn she uses.

So, this statement is what the slope tells you about the situation:

green checkmark, Sandra needs 2 tablespoons of sugar for every 3 cups of popcorn.

These statements are not what the slope tells you about the situation:

red X symbol, Sandra needs 1 tablespoon of sugar for every cup of popcorn.

red X symbol, Sandra needs 1 tablespoon of sugar for every 3 cups of popcorn.

red X symbol, Sandra needs 3 tablespoons of sugar for every 2 cups of popcorn.

Looking for more? Try these:

Lesson: Linear functions

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Not feeling ready yet? These can help:

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

CC.4Interpret points on the graph of a linear function

Lesson: Linear functions

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