A table has (x, y) pairs (2, 6), (4, 12), and (5, 15). Find k.
- Calculate 6/2 = 3, 12/4 = 3, and 15/5 = 3.
- All ratios agree, so y = 3x.
Answer: k = 3
Constant of Proportionality Worksheets
Use equivalent ratios and unit rates to solve proportional relationships.
Learn the skill
Finding the constant of proportionality
In a proportional relationship, y = kx. The constant k is the amount of y per one unit of x. In a table, every nonzero x gives the same ratio y/x; on a graph, the points lie on a straight line through the origin.
A method you can use
- Decide which quantity is x and which is y, including their units.
- For each nonzero x, calculate y ÷ x and check that the ratio stays constant.
- Write y = kx and interpret k in the context. A nonzero starting fee means the relationship is not proportional.
Worked examples
Three notebooks cost $7.50 at a constant price per notebook. Write cost C in terms of number n.
- Divide total cost by number: 7.50 ÷ 3 = 2.50 dollars per notebook.
- Multiply that unit price by n.
Answer: C = 2.50n
A straight-line graph passes through (0, 0) and (4, 10). Find its proportional constant.
- The origin confirms there is no starting offset.
- Use the other point: k = 10/4 = 2.5.
Answer: k = 2.5
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. For y = 7x, what is the constant of proportionality?
Show answer and explanation
7
The coefficient of x in y = kx is k.
2. A proportional table contains (2, 9) and (6, 27). Find k.
Show answer and explanation
4.5
9 ÷ 2 and 27 ÷ 6 both equal 4.5.
Before you begin
Multiply, divide and simplify fractions. Read quantities with their units.
Choose your level
- Easy: Use whole-number rates and small factors.
- Medium: Find missing values in equivalent ratios.
- Hard: Use two steps or reverse a relationship.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
In a proportional relationship y = kx, x = 3 gives y = 15. Find k.
2
In a proportional relationship y = kx, x = 6 gives y = 24. Find k.
3
In a proportional relationship y = kx, x = 7 gives y = 14. Find k.
4
In a proportional relationship y = kx, x = 6 gives y = 18. Find k.
5
In a proportional relationship y = kx, x = 8 gives y = 32. Find k.
6
In a proportional relationship y = kx, x = 2 gives y = 8. Find k.
Answer Key
1. 52. 43. 24. 35. 46. 4