1. Constant of Proportionality

2. Launch
The car paint company provides a perplexing pay graph for new managers.
What does the graph show?
Which point—A, B, or C—might be the most useful? Explain.

3. Constant of Proportionality
Recall that two quantities x and y have a proportional relationship if y is always a constant multiple of x.
This constant multiple is called the constant of proportionality.
The constant of proportionality is the ratio where x is the independent variable and
y is the dependent variable.
If x and y have different units, then the constant of proportionality can be written as a unit rate. y x __

4. The Constant of Proportionality
The Constant of Proportionality is represented as k.
The formula to find the Constant of Proportionality is
k = OR y = kx y x __

5. Constant of Proportionality Video

6. Constant of Proportionality
There is one brick with a length of 20 centimeters.
The proportion total length (cm) to number of bricks is 20:1 .
So, the constant of proportionality or unit rate is 20.

7. Constant of Proportionality
The weight of the stack depends on the number of books in the stack. Identify the constant of proportionality for this situation.
Then use the constant of proportionality to find the weight of 11 books.

8. Constant of Proportionality
Each shoebox is the same height. The height of the display depends on the number of shoeboxes in one column of shoeboxes.
What is the constant of proportionality for this situation?

9. Constant of Proportionality
You have a recipe that calls for 2 cups of flour to make 3 dozen cookies. Your friend has a cookie recipe that calls for 3 cups of flour to make 60 cookies.
Are the constants of proportionality the same for the two recipes?
Are the recipes for the same cookie?
How do you know?

10. Constant of Proportionality
You run on a treadmill daily at a constant speed. On Monday, you ran 2.25 miles in 22.5 minutes. On Tuesday, you ran 2.35 miles in 25 minutes.
Are the constants of proportionality the same for the two days?
How do you know?

11. Constant of Proportionality
The table shows the amount of money raised based on the number of tickets sold for a charity concert.
Does the table show a constant of proportionality? If so, what is the constant of proportionality for this situation?
You can sell no more than 2,500 tickets for the concert. Find the maximum amount of money the fundraiser can raise.

12. Constant of Proportionality
The table shows the time it takes to pump gasoline based on the number of gallons pumped.
What is the constant of proportionality for this situation?

13. Constant of Proportionality
The graph shows the number of times a male hummingbird beats its wings based on time.
What is the constant of proportionality for this situation?
What does the point (1, 80) represent?

14. Constant of Proportionality
The graph shows the distance a cyclist traveled based on time.
What is the constant of proportionality for this situation?

15. Focus Question What is a constant of proportionality?
The constant of proportionality describes the relationship between two quantities that have a proportional relationship.
What does the constant of proportionality tell you?
It is the ratio y to x, or a unit rate. It tells you the constant multiple between the two quantities.

16. Homework:
Constant of Proportionality Worksheet