Lesson 12: Constant of Proportionality and the Equation Y ...

[Pages:5]Name:_________________________________ Accordino-Math 7

M1AL12

Date:_________ Period:________

Lesson 12: Constant of Proportionality and the Equation Y=kx. Bellringer

1. (2 pts) Fill in the table using the given values to create quantities proportional to each other, then graph them.

1

4

2

4

Name:_________________________________ Accordino-Math 7

M1AL12

Date:_________ Period:________

Lesson 12: Constant of Proportionality and the Equation Y=kx. Notes

A Directly Proportional Relationship has a linear equation of the form

y kx

Y

The ratio is called the _________________ _______________________________ and represented by the variable

X

K.

To formulate the equation for a proportional relationship:

Y

1) Determine the constant of proportionality or unit rate for the problem by evaluating the ratio, and

X assign that value to the variable k.

2) Determine the independent and dependent variable for the problem. The independent variable is the

variable x , and the dependent variable is the variable y .

3) Put in the form, y kx .

Example 1: Write an equation that will model the proportional relationship given in each graph below and explain what the equation means in a statement.

a.

b.

Example 2: Write an equation that will model the proportional relationship given in each real world situation.

2. There are 3 cans that store 9 tennis balls. Consider the number of balls per can. a. Find the constant of proportionality for this situation. What does it mean for this situation? b. Write an equation to represent the relationship.

Name:_________________________________

M1AL12

Date:_________

Accordino-Math 7

Period:________

3. In 25 minutes Li can run 10 laps around the track. Consider the number of laps she can run per minute. a. Find the constant of proportionality in this situation. What does it mean for this situation?

b. Write an equation to represent the relationship.

Example 3: Determine the equation for each situation below and use it to answer the question in part c. Situation 1: Bananas are $0.59/pound.

a. What is the constant of proportionality?

b. What is the equation that models the relationship between total price for bananas?

c. How much does 25 pounds of bananas cost?

4. The dry cleaning fee for 3 pairs of pants is $18. a. What is the constant of proportionality? b. What is the equation that models the relationship between total price for dry cleaning pants?

c. How much will the dry cleaner charge for 11 pairs of pants?

Example 5: Andrea's Portraits Andrea is a street artist in New Orleans. She draws caricatures (cartoon-like portraits of tourists). People have their portrait drawn and then come back later to pick it up from her. The graph below shows the relationship between the number of portraits she draws and the amount of time in hours needed to draw the portraits.

a. Write several ordered pairs from the graph and explain what each coordinate pair means in the context of this graph.

b. Determine the constant of proportionality and explain what it means in this situation.

c. Write an equation that will model the proportional relationship given in each real world situation.

Name:_________________________________

M1AL12

Date:_________

Accordino-Math 7

Period:________

Homework:

1) John and Amber work at an ice cream shop. The hours worked and wages earned are given for each person.

John's wages

Time (h) Wages ($)

2

18

3

27

4

36

a. Are John's wages proportional to time. How do you know? If they are, determine the unit rate.

b. Are Amber's wages proportional to time. How do you know? If they are, determine the unit rate.

c. Write an equation to model the relationship between each person's wages. Identify the constant of proportionality for each.

d. How much would each worker make after working 10 hours? Who will earn more money?

2) It cost $5 to send 6 packages through a certain shipping company. Consider the number of packages per dollar.

i. Find the constant of proportionality for this situation. ii. Write an equation to represent the relationship.

Name:_________________________________ Accordino-Math 7

M1AL12

Date:_________ Period:________

Lesson 12: Constant of Proportionality and the Equation Y=kx. Bellringer

1) Write an equation that will model the proportional relationships shown in the graph below graph.

2) (2 pts) Jennifer is shopping with her mother. They pay $2 per pound for tomatoes at the vegetable stand. a. Write an equation to represent the proportional relationship.

b. How much will Jennifer pay if she buys 5.3 pounds of tomatoes?

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