Constant of Proportionality from an Equation Worksheet for 12-Year-Olds | Math

Instructions

1. The constant of proportionality tells how much one quantity changes for every 1 unit of another quantity.
2. In an equation written as y = kx, the number k is the constant of proportionality.
3. For each problem, identify k and explain what it means when appropriate.
4. Show your work. Use the hint when you need support.

Example:

For the equation y = 4x, the constant of proportionality is 4.

This means that y is 4 times x, or y increases by 4 for every 1 increase in x.

Part 1: Find the Constant

Find the constant of proportionality in each equation.

1. y = 6x

   k = __

2. y = 9x

   k = __

3. y = 0.5x

   k = __

4. y = 12x

   k = __

5. y = 3.25x

   k = __

6. y = 1/4x

   k = __

Hint: Look for the number multiplying x.

Part 2: Multiple Choice

Circle the best answer.

7. What is the constant of proportionality in y = 15x?

• A. 1
• B. 15
• C. x
• D. y

8. What is the constant of proportionality in y = 0.75x?

• A. 0.075
• B. 7.5
• C. 0.75
• D. 75

9. Which equation has a constant of proportionality equal to 8?

• A. y = x + 8
• B. y = 8x
• C. y = 8 + x
• D. x = 8y

10. In the equation y = 2.5x, what does 2.5 represent?

• A. The starting amount
• B. The value of y
• C. The constant of proportionality
• D. The value of x

Part 3: Match the Equation to Its Constant

Write the letter of the correct constant in each blank.

Choices:

• A. 14
• B. 0.2
• C. 3/5
• D. 1.5
• E. 7

Part 4: Complete the Table

Each equation shows a proportional relationship. Find the constant of proportionality and complete the missing values.

Example: For y = 4x, the constant is 4. If x = 3, then y = 4(3) = 12.

Part 5: Real-World Proportions

Show an equation and identify the constant of proportionality for each situation.

21. A music service charges $6 for every month of membership. Let m represent the number of months and c represent the total cost.

    a. Write an equation for the total cost: __

    b. What is the constant of proportionality? __

22. A cyclist travels 18 miles every hour. Let h represent hours and d represent distance in miles.

    a. Write an equation for the distance: ____

    b. What is the constant of proportionality? __

    c. What does the constant mean in this situation? _____

    ---

23. A recipe uses 2 cups of flour for every batch of muffins. Let b represent batches and f represent cups of flour.

    a. Write an equation: ___

    b. What is the constant of proportionality? __

    c. How much flour is needed for 7 batches? ___

Part 6: Is It Proportional?

A proportional relationship can be written in the form y = kx, with no added or subtracted starting amount.

For each equation, write Yes or No. If the relationship is proportional, give the constant of proportionality.

24. y = 11x

    Proportional? __ k = __

25. y = 4x + 2

    Proportional? __ k = __

26. y = x/3

    Proportional? __ k = __

27. y = 9 - 2x

    Proportional? __ k = __

28. y = 0.8x

    Proportional? __ k = __

Part 7: Explain Your Thinking

29. A student says that the constant of proportionality in y = 13x is 13x. Is the student correct? Explain your answer.

30. Write your own proportional equation with a constant of proportionality of 6. Then explain what the 6 means.

Equation: __

Explanation: ___

Optional Challenge

31. The equation y = kx represents a proportional relationship. If x = 8 and y = 52, find k.

Show your work:

Answer: k = __

32. A store sells notebooks at the same price. The equation c = 2.75n gives the cost c for n notebooks.

    a. What is the constant of proportionality? __

    b. What is the cost of 10 notebooks? _____

    c. How many notebooks can be bought for $22? _____

Answer Key

1. 6
2. 9
3. 0.5
4. 12
5. 3.25
6. 1/4
7. B. 15
8. C. 0.75
9. B. y = 8x
10. C. The constant of proportionality
11. E. 7
12. B. 0.2
13. A. 14
14. D. 1.5
15. C. 3/5
16. k = 5; y = 10
17. k = 10; x = 7
18. k = 0.5; y = 4
19. k = 3; x = 9
20. k = 1.25; y = 5
21. a. c = 6m; b. 6; the service costs $6 per month.
22. a. d = 18h; b. 18; c. The cyclist travels 18 miles per hour.
23. a. f = 2b; b. 2; c. 14 cups
24. Yes; k = 11
25. No; there is an added starting amount of 2, so it is not in the form y = kx.
26. Yes; k = 1/3
27. No; the equation has a starting amount of 9 and is not in the form y = kx.
28. Yes; k = 0.8
29. No. The constant of proportionality is 13 because it is the number multiplying x. The expression 13x represents the value of y, not just the constant.
30. Answers will vary. Example: y = 6x; 6 means y is 6 times x, or y increases by 6 for every 1 increase in x.
31. k = y/x = 52/8 = 6.5
32. a. 2.75; b. $27.50; c. 8 notebooks