Recognizing Proportional Relationships Worksheets, Grade 7 (7.RP.A.2) – Free PDF + Answer Key

First page of the recognizing proportional relationships practice worksheet

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PDFs print on US Letter paper. Free for classroom and home use.

Step-by-step math videos on the Math With Mr DJ YouTube channel →

Key idea

Proportional means y ÷ x is constant for every pair. Call that constant k and the rule is y = kx. Equivalent test: the graph passes through (0, 0). Steady growth alone is not enough.

Sample problems

For the pair (2, 6), find y ÷ x.
For the pair (3, 9), find y ÷ x.
For the pair (5, 15), find y ÷ x.
Those three pairs are proportional. Using k from above, find y when x = 10.

Common mistakes to watch for

Checked only the first pair. One matching ratio proves nothing — you need them all.
Answered yes because y increases by 2 every time. A constant DIFFERENCE is not a constant RATIO.
Said it is proportional because the graph is a straight line. Straight is necessary but not sufficient; it must also pass through (0, 0).

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

Teach with the slides (about 15 minutes), or watch the video together.
Practice with the worksheet. Questions climb from fluency to application to reasoning.
Check understanding with the exit ticket, and send the homework home.
Mark with the answer key — each answer shows the steps and the most likely mistake.