Write an equation in the form y = kx for this table.
x1245y361215
Table to equation · grades 6–7
Write Proportional Equations from Tables
Move from matching values to a general rule. Each table has one exact constant of proportionality, and the answer key states the relationship in the form y = kx.
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Write y = kx from Tables
Table to y = kx · Small whole numbers · Seed 261501
Write an equation in the form y = kx for this table.
x2345y8121620
Write an equation in the form y = kx for this table.
x2345y46810
Write an equation in the form y = kx for this table.
x1345y26810
Write an equation in the form y = kx for this table.
x1235y36915
Write an equation in the form y = kx for this table.
x2345y10152025
Write an equation in the form y = kx for this table.
x1235y5101525
Write an equation in the form y = kx for this table.
x1345y391215
Write an equation in the form y = kx for this table.
x1245y24810
Write an equation in the form y = kx for this table.
x1345y6182430
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.
Writing y = kx from a table
Find k first by dividing y by x in one row, then write y = kx with that number in place of k. Test the equation on a different row: if it gives every y-value in the table, the rule is right. A proportional equation passes through the origin, so a rule with an added number, such as y = 3x + 2, describes a different kind of relationship.
Worked examples
- x = 2, 4, 6 and y = 14, 28, 42. k = 14 ÷ 2 = 7, so y = 7x. Check another row: 7 × 4 = 28 and 7 × 6 = 42.
- x = 1, 2, 3 and y = 9, 18, 27. k = 9 ÷ 1 = 9, so y = 9x. With x = 10 the rule predicts y = 90.
- Tickets: 2 tickets cost $18 and 5 tickets cost $45. k = 18 ÷ 2 = 9, so y = 9x, and 8 tickets cost 9 × 8 = $72.
- Not proportional: x = 1, 2, 3 and y = 5, 7, 9 follows y = 2x + 3. At x = 0 it would give 3, not 0, so it is not of the form y = kx.
Common slips
- Writing x = ky. For x = 2 and y = 14 the rule is y = 7x, not x = 7y.
- Using a y-value as k. In the first example k is 7, not 14 or 42.
- Using the difference between rows. The y-values 14, 28, 42 step by 14, but k is 7.
- Skipping the check. Substitute a second row into the equation before calling it finished.
How to use this worksheet
Have students show three lines for each table: the division that finds k, the equation y = kx, and a check on a second row. The answer key states the equation in that form so students can compare their notation as well as the number.
Common Core connection
- 7.RP.A.2.c · Represent proportional relationships with equations and connect each variable to its meaning.
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.
Teaching note 1
Find k first; then substitute it into y = kx.
Teaching note 2
Use one table row to verify that the equation produces the listed y-value.
Teaching note 3
Test the finished equation on a row you did not use to find k; it must reproduce every pair in the table.
Teaching note 4
The variable names are intentionally consistent so students can focus on the relationship rather than a notation switch.
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
Frequently asked questions
What does k represent?
It represents the amount of y for one unit of x—the constant rate or unit rate.
Can a proportional equation have a plus sign?
No. A relationship in the form y = kx passes through the origin; an added constant represents a different situation.
Which standard does this practice?
CCSS 7.RP.A.2c: represent a proportional relationship by an equation, typically in the form y = kx.
How is this different from finding the constant of proportionality?
Finding k is step one. This skill goes further and states a general rule y = kx that predicts any y from any x, not only the rows shown.