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

At the Pineville County Fair popcorn stand, Vivian scoops popcorn from a large container to fill smaller bags to sell. As she fills the bags, the amount of popcorn in the container decreases.

This situation can be modeled as a linear relationship.

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

There are 50 scoops of popcorn in the container to start.

Vivian fills each bag with 2 scoops of popcorn.

Vivian fills each bag with 5 scoops of popcorn.

Vivian fills 20 bags of popcorn.

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Learn with an example

question

Brooke orders a large box of apples to make apple pies for the Fairview Food Festival. Brooke takes apples from the box to make each pie.

This situation can be modeled as a linear relationship.

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

Brooke buys 120 apples.

Brooke uses 1 apple for every 5 pies she bakes.

Brooke uses 5 apples for every pie she bakes.

Brooke has 60 apples left after she has baked 12 pies.

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

(

100

)

and

(

)

Now, calculate the slope.

slope

change in

–

100

–

The slope of the line relates a change in the number of apples Brooke has left to a change in the number of pies she has baked. So, the slope

–

tells you that the number of apples Brooke has left decreases by 5 for every 1 pie she bakes.

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

green checkmark, Brooke uses 5 apples for every pie she bakes.

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

red X symbol, Brooke buys 120 apples.

This statement is true, but this is what the -intercept, , tells you about the situation.

red X symbol, Brooke uses 1 apple for every 5 pies she bakes.

This statement is false. Brooke uses 5 apples for every pie she bakes.

red X symbol, Brooke has 60 apples left after she has baked 12 pies.

This statement is true, but this is what the point tells you about the situation.

Looking for more? Try these:

Lesson: Linear functions

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W.6Constant rate of change: graphs

N.10Interpret graphs of proportional relationships

Lesson: Linear functions

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