IXL - Interpret the slope and y-intercept of a linear function (Algebra 2 practice)

Kendrick is tie-dyeing T-shirts with his friends. To make purple dye, he mixes drops of red dye with drops of blue dye. The number of red drops Kendrick uses depends on the number of blue drops he uses.

This situation can be modeled as a linear relationship.

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

Kendrick uses 1 red drop for every 4 blue drops.

Kendrick uses 4 red drops for every 1 blue drop.

Kendrick uses 1 red drop for every 5 blue drops.

Kendrick uses 5 red drops for every 1 blue drop.

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Learn with an example

question

During the winter, Dan drives a truck that uses a device to spread salt on icy roads. As he drives, the amount of salt in the truck decreases.

This situation can be modeled as a linear relationship.

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

After covering 12 miles of icy road, the truck has 800 pounds of salt left.

The truck has 1,600 pounds of salt to start.

The truck spreads 200 pounds of salt every 3 miles.

The truck spreads 200 pounds of salt every 9 miles.

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

(

1,600

)

and

(

1,200

)

Now, calculate the slope.

slope

change in

1,200

–

1,600

–

400

–

200

The slope of the line relates a change in the amount of salt in the truck to a change in the length of icy road the truck has covered. So, the slope

–

200

tells you that the amount of salt in the truck decreases by 200 pounds for every 3 miles of icy road covered.

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

green checkmark, The truck spreads 200 pounds of salt every 3 miles.

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

red X symbol, After covering 12 miles of icy road, the truck has 800 pounds of salt left.

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

red X symbol, The truck has 1,600 pounds of salt to start.

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

red X symbol, The truck spreads 200 pounds of salt every 9 miles.

This statement is false. The truck spreads 200 pounds of salt every 3 miles.

Looking for more? Try these:

Lesson: Linear functions

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Work it out

Not feeling ready yet? These can help:

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

N.4Evaluate a linear function from its graph: word problems

Lesson: Linear functions

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