Find the constant of proportionality, k = y/x.
x1245y361215
Unit rate from tables · grades 6–7
Constant of Proportionality from Tables
Generate focused practice for finding k in y = kx from equivalent-ratio tables. Every row is constructed from one whole-number unit rate, so k is never inferred from rounding.
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Constant of Proportionality
Find k from tables · Small whole numbers · Seed 261501
Find the constant of proportionality, k = y/x.
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Find the constant of proportionality, k = y/x.
x2345y46810
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x1235y36915
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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.
Finding the constant of proportionality from a table
The constant of proportionality, k, is the number you multiply x by to get y, so k = y ÷ x. It is also the unit rate: the amount of y for one unit of x. Pick a row with a nonzero x, divide, then confirm with a second row. In a cost table k is dollars per item, and in a distance table it is miles per hour, so name the units along with the number.
Worked examples
- Cost: 3 notebooks cost $6 and 5 notebooks cost $10. 6 ÷ 3 = 2 and 10 ÷ 5 = 2, so k = 2 dollars per notebook.
- Distance: x = 2, 4, 6 hours and y = 150, 300, 450 miles. 150 ÷ 2 = 75, 300 ÷ 4 = 75 and 450 ÷ 6 = 75, so k = 75 miles per hour.
- A table that does not start at 1: x = 3, 6, 9 and y = 12, 24, 36. 12 ÷ 3 = 4, so k = 4. The table never shows x = 1, but k tells you y would be 4 there.
- Using k: if k = 4 and x = 10, then y = 4 × 10 = 40.
| Batches (x) | Flour (y, cups) | y ÷ x (cups per batch) |
|---|---|---|
| 2 | 8 | 4 |
| 3 | 12 | 4 |
| 5 | 20 | 4 |
Each row gives the same rate, so k = 4 cups per batch and the relationship is y = 4x.
Common slips
- Dividing x by y. For the pair 3 and 12 that gives 0.25 instead of 4. Ask which quantity is being found per one of the other.
- Using the difference between rows. In the table x = 3, 6 and y = 12, 24 the y-values differ by 12, but k is 4.
- Leaving off the units. 'k = 2' says little; 'k = 2 dollars per notebook' answers the question.
- Testing one row only. Check a second row before stating k, because one pair cannot show that the whole table is proportional.
How to use this worksheet
Ask students to write k with its units beside each table and to name the row they used to check it. The answer key lists k and the matching unit rate, which makes it quick to find whether a mistake came from the division or from the units.
Common Core connection
- 7.RP.A.2.b · Identify the constant of proportionality in tables, graphs, equations, and verbal descriptions.
- 7.RP.A.1 · Compute unit rates associated with ratios of fractions, including rates with unlike units.
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.
Note 1
Divide y by x to find k, then check it against a different row.
Note 2
The constant of proportionality is also the unit rate: the y-value when x equals 1.
Note 3
k carries units. In a cost table it is dollars per item, and naming those units keeps the number meaningful.
Note 4
When a table starts at x = 2 or x = 3, division still reveals the per-one value.
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
Quick answers
Is k always an integer here?
Yes. This focused version uses whole-number k values so the lesson tests proportional structure, not fraction division.
Why check a second row?
A second check prevents students from treating one pair as proof when the full table might not be proportional.
Which standard does this practice?
CCSS 7.RP.A.2b: identify the constant of proportionality (unit rate) from a table, and 7.RP.A.2d, interpreting the point (1, r).
How is this different from writing y = kx?
Here the work stops at the number k and its meaning as a unit rate. The 'write proportional equations' skill takes that k and builds the general rule y = kx.