Constant of Proportionality Review

Unit Rates

100

A pack of 8 pencils costs $4. What is the cost per pencil?

Answer: $0.50

200

A car travels 180 miles in 3 hours. What is its unit rate?

Answer: 60 miles per hour

300

12 notebooks cost $30. Find the cost of one notebook.

Answer: $2.50

400

Maria earns $84 for working 7 hours. What is her hourly wage?

Answer: $12 per hour

500

A faucet fills 18 gallons in 6 minutes. At this rate, how many gallons fill in 15 minutes?

Answer: 45 gallons

Constant of Proportionality

100

If y=5xy=5x, what is the constant of proportionality?

Answer: 5

200

x                                       y

2                                      12

4                                      24

Find k.

Answer: 6

300

x                                       y

3                                      15

5                                      25

8                                     40

Find the constant of proportionality.

Answer: 5

400

The equation is

y=9x

What does the 9 represent?

Answer: The constant of proportionality (9 units of y for every 1 unit of x).

500

If k=4.5, write an equation representing the relationship.

Answer: y=4.5x

Is It Proportional?

100

x                             y

1                             3

2                             6

3                             9

Is it proportional?

Answer: Yes

200

x                             y

2                             5

4                             10

6                             14

Is it proportional?

Answer: No

300

Does the graph pass through the origin?

Answer: Yes → proportional.

400

True or False:

Every proportional relationship has a constant rate.

Answer: True

500

Daily Double #1:

Explain why a graph that doesn't pass through the origin cannot represent a proportional relationship.

Answer:
A proportional relationship must pass through the origin (0,0) because when there are 0 of one quantity, there must be 0 of the other quantity. If the graph does not pass through the origin, the relationship has a starting value that is not zero, so it is not proportional.

Real-World Problems

100

5 tacos cost $15.

Find the unit price.

Answer: $3

200

A printer prints 48 pages in 6 minutes.

How many pages per minute?

Answer: 8

300

A babysitter earns $56 in 4 hours.

Write an equation.

Answer: y=14x

400

Gas costs $4.25 per gallon.

How much do 9 gallons cost?

Answer: $38.25

500

You buy 12 pounds of apples for $30.

How much would 18 pounds cost?

Answer: $45

Mixed Challenge

100

What is another name for the constant of proportionality?

Answer: Unit rate

200

Complete the equation:

y=kx

What does k stand for?

Answer: Constant of proportionality

300

Daily Double #2:

Write a real-world scenario with a unit rate of 12.

Possible Answer:
A babysitter earns $12 per hour. The unit rate is $12 for every 1 hour.

Other acceptable examples:

• A car travels 12 miles per hour.
• Apples cost $12 per pound.
• A machine makes 12 bottles every minute.

400

A recipe uses 6 cups of flour for 3 batches.

How much flour for 8 batches?

Answer: 16 cups

500

Create a proportional relationship with a constant of proportionality of 7.

Possible Answer:

• Table: (1,7), (2,14), (5,35)
• Equation: y=7x