Is y/x constant in every row?
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Equivalent ratios in a table · grades 6–7
Identify Proportional Relationships from Tables
Build table sets that require a real proportionality check instead of pattern guessing. Some tables preserve one constant y/x; others deliberately change one row so students must identify the broken relationship.
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Identify Proportional Tables
Identify proportional tables · Small whole numbers · Seed 261501
Is y/x constant in every row?
x1345y381215
Is y/x constant in every row?
x1345y5152025
Is y/x constant in every row?
x1235y36914
Is y/x constant in every row?
x1245y22810
Is y/x constant in every row?
x1345y6192430
Is y/x constant in every row?
x1245y6122430
Is y/x constant in every row?
x1245y6122230
Is y/x constant in every row?
x1245y461620
Is y/x constant in every row?
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No fake precision: tables, graph points, equations, and double number lines come from the same exact whole-number constant of proportionality. Better Buy problems compare integer cents per item, so a winner is never chosen from a rounded display value.
How to tell if a table is proportional
Divide y by x in every row. If every row gives the same number, the table is proportional and that number is the constant of proportionality, k. If even one row gives a different quotient, the table is not proportional. Compare with multiplication and division, not with how fast y grows: a table can climb steadily and still fail the test. Each proportional table here is built from one exact whole-number k, and each non-proportional table is made by changing one y-value, so the answer key can point to the first row that breaks the pattern.
Worked examples
- Proportional: x = 2, 4, 6, 8 and y = 10, 20, 30, 40. Dividing gives 10 ÷ 2 = 5, 20 ÷ 4 = 5, 30 ÷ 6 = 5 and 40 ÷ 8 = 5. Every row gives 5, so the table is proportional and k = 5.
- Not proportional: x = 1, 2, 3, 4 and y = 3, 5, 7, 9. Dividing gives 3, 2.5, about 2.33 and 2.25. The quotients change, so the table is not proportional even though y goes up by 2 each time.
- A zero row: if a table has x = 0 and y = 0, skip that row when dividing, because you cannot divide by 0, and test the other rows.
- Equations follow the same test. For y = -2x, y ÷ x is -2 for every x, so it is proportional with k = -2. For y = 2x + 1, y ÷ x changes from row to row, so it is not.
| x | y | y ÷ x |
|---|---|---|
| 2 | 6 | 3 |
| 4 | 10 | 2.5 |
| 6 | 18 | 3 |
| 8 | 24 | 3 |
The quotient changes in the second row, so the table is not proportional—even though the last rows return to 3.
Mistakes that make a table look proportional
- Checking only the first row. One matching ratio proves nothing; the test is every row.
- Looking at differences. In x = 1, 2, 3 and y = 4, 7, 10, y rises by 3 each time, but 4 ÷ 1 = 4 and 7 ÷ 2 = 3.5, so the table is not proportional.
- Flipping the ratio in some rows. Choose y ÷ x or x ÷ y and use the same one in every row.
- Assuming a table with the point (0, 0) is automatically proportional. The zero row fits, but the other rows still have to match.
How to use this worksheet
Print a set, have students write the quotient beside each row, and circle the first row that breaks the pattern. Then ask for one sentence explaining why the table is or is not proportional. The New problems button builds a fresh set, and the answer key shows the quotient for every row.
Common Core connection
- 7.RP.A.2 · Recognize and represent proportional relationships using tables, graphs, equations, and descriptions.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Teacher tip 1
A table is proportional only when the ratio y/x is the same for every nonzero x-value.
Teacher tip 2
A growing pattern alone is not proof; compare multiplicatively rather than looking only at additive differences.
Teacher tip 3
The quick test is y divided by x on every row: if two rows give different quotients, the table is not proportional.
Teacher tip 4
Use the answer key to discuss the first row that breaks the constant ratio.
Move among tables, equations, graphs, double number lines, and Better Buy decisions in one exact generator.
Return to ratio foundations →Practice simplified ratios, equivalent tables, unit rates, proportions, and percent proportions.
More skills in this set
Common questions
How are non-proportional tables made?
They begin with an exact y = kx relationship, then one y-value is changed so the table cannot accidentally remain proportional.
Does every proportional table include a zero row?
No. Students can establish the relationship from matching nonzero ratios; the coordinate origin is emphasized in the graph-focused practice.
Which standard does this practice?
CCSS 7.RP.A.2a: decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table.
How do you know if a table is not proportional?
Divide y by x in every row. If any two rows give different quotients, the table is not proportional. For x = 2, 4, 6 and y = 6, 10, 14 the quotients are 3, 2.5 and about 2.33, so it fails even though y keeps rising.
Can a table that keeps increasing still be non-proportional?
Yes. The pairs 1 to 3, 2 to 5, 3 to 7 rise steadily, but y over x changes from 3 to 2.5 to about 2.33, so it is not proportional.