Proportional relationships worksheets
Fifty problems on proportional relationships: finding k, using y = kx and spotting proportional relationships.
Each question builds on the idea that y ÷ x is the same for every pair.
Download the free proportional relationships worksheet (PDF)
Proportional relationships worksheet
What’s on the worksheet
- 50 questions on proportional relationships, sized for US Letter paper
- 5 pages of questions plus an answer key on the last page
- Written for grade 7, matching Common Core 7.RP.A.2
- Name and date lines at the top, and room to show the work
Sample questions from this worksheet
- y is proportional to x. When x = 9, y = 63. Find the constant of proportionality k.
- y is proportional to x. When x = 2, y = 8. Find k.
- y is proportional to x. When x = 4, y = 12. Find k.
- y is proportional to x. When x = 2, y = 14. Find y when x = 4.
- y is proportional to x. When x = 7, y = 21. Find y when x = 2.
- Is the relationship in a table proportional? Explain.
Quick reference: proportional relationships
Two amounts are proportional when y ÷ x is the same for every pair. That number is the constant of proportionality, k, and the equation is y = kx.
- Table: divide each y by its x. Equal answers mean proportional.
- Graph: a straight line through (0, 0).
- Equation: y = kx with nothing added. y = 2x + 3 is not proportional.
See the proportional relationships lesson and the constant of proportionality lesson for graphs and a quiz.
Preview the worksheet and answer key
Make a new proportional relationships worksheet
Need another page for extra practice, a retake or a second group in class? The free Mathify Kids test maker builds a fresh proportional relationships worksheet with different numbers every time. Choose how many questions, print it with its own answer key, or let your child take it on screen and see the score straight away.
Proportional relationships: a worked example (y is proportional to x. When x = 4, y = 12. Find k.)
- In a proportional relationship, y = kx.
- So k = y ÷ x = 12 ÷ 4.
- k = 3, so the equation is y = 3x.
- Check: when x = 4, y = 3 × 4 = 12.
How to use it at home and in class
At home
Ask everyday questions: is the cost of apples proportional to their weight? Is a taxi fare with a starting charge proportional to the distance? Ten problems a day works better than a whole sheet at once. Mark them together with the answer key, then ask your child to explain one they got wrong: finding the mistake themselves is where the learning happens.
In class
Use the first row as a warm-up, a full page for independent practice, or five questions as an exit ticket. For a retake or a second group, make a new version with the test maker so every child gets different numbers.
Mistakes to watch for
- Dividing x by y instead of y by x.
- Calling any straight line proportional, even if it misses (0, 0).
- Finding k from one row without checking the others.
What to practice before and after proportional relationships
- Before: unit rates. If this sheet is a struggle, go back a step.
- After: solving proportions, once this one is mostly right.
- Learn it first: the proportional relationships lesson.
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Questions parents ask
What is the constant of proportionality?
The number k in y = kx. It is the value of y when x is 1, which is the unit rate.
What grade is this proportional relationships worksheet for?
It is written for grade 7 and matches Common Core standard 7.RP.A.2.
Can I get a different version of this proportional relationships worksheet?
Yes. Use the free Mathify Kids test maker to make a new proportional relationships worksheet with different numbers every time, with its own answer key.