Practice: Proportional Relationships

Part A: Identifying Proportional Relationships from Tables

Directions: Determine if each table shows a proportional relationship. If yes, find k and write the equation y = kx.

1. Bananas cost a certain amount per pound.

Pounds (x)	1	2	3	4
Cost (y)	$0.60	$1.20	$1.80	$2.40

Proportional? _______ k = _______ Equation: y = _______

2. A taxi charges a base fee plus a rate per mile.

Miles (x)	0	1	2	3
Cost (y)	$3	$5	$7	$9

Proportional? _______ Explain: _________________________________

3. A factory produces widgets per hour.

Hours (x)	2	5	8	10
Widgets (y)	50	125	200	250

Proportional? _______ k = _______ Equation: y = _______

Part B: Finding the Constant of Proportionality

Directions: Find k (the constant of proportionality) from each representation.

4. From the equation: y = 7x

k =

5. From the equation: y = (1/4)x

k =

6. A graph passes through (3, 18).

k = y/x =

7. A graph passes through (8, 6).

k = y/x =

Part C: Writing Equations for Proportional Relationships

Directions: Write an equation in the form y = kx for each situation.

8. A car gets 32 miles per gallon.

(Let x = gallons, y = miles)

y =

9. You earn $14.50 per hour.

(Let x = hours, y = earnings)

y =

10. There are 12 eggs per carton.

(Let x = cartons, y = eggs)

y =

11. A printer prints 25 pages per minute.

(Let x = minutes, y = pages)

y =

Part D: Identifying Proportional Equations

Directions: Circle YES if the equation represents a proportional relationship, or NO if it does not.

Equation	Proportional?	Explain Why or Why Not
12. y = 6x	YES / NO
13. y = x + 5	YES / NO
14. y = 2.5x	YES / NO
15. y = 4x - 4	YES / NO
16. y = x/3	YES / NO

Part E: Word Problems

Directions: Read each problem carefully. Show your work.

17. The distance a turtle crawls is proportional to time. In 4 minutes, the turtle crawls 12 feet.

a) What is the constant of proportionality? k = _______

b) Write an equation: y = _______

c) How far will the turtle crawl in 10 minutes? _______

18. A recipe uses 3 cups of flour for every 2 cups of sugar. Is this relationship proportional? If yes, find k (flour per sugar).

Answer: _________________________________

19. The graph of a proportional relationship passes through (5, 35). Write the equation and find y when x = 12.

k = _______ Equation: y = _______ When x = 12, y = _______

20. Movie tickets cost $9.50 each. Is the total cost proportional to the number of tickets? Write an equation and find the cost of 8 tickets.

Proportional? _______ Equation: _______ Cost of 8 tickets: $_______

Challenge: Think About It!

21. Jake says the relationship between the side length and perimeter of a square is proportional. Maria says it's not. Who is correct? Explain using a table or equation.

22. Two runners are training. Runner A: y = 8x (miles per hour). Runner B travels 42 miles in 6 hours. Which runner is faster? Explain.