Is the graphed relationship proportional? Explain using the straight-line and origin test.
Check both conditions: straight line and through the origin.
CCSS 7.RP.A.2a · graph proportionality
Identify Proportional Relationships from Graphs
Students decide whether a graphed relationship is proportional instead of relying only on tables. Non-proportional examples can still be perfectly linear, forcing the key distinction: a proportional line must pass through the origin.
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Identify Proportional Graphs
Identify proportional graphs · Grade 7 standard · Seed 261601
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Is the graphed relationship proportional? Explain using the straight-line and origin test.
Check both conditions: straight line and through the origin.
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Is the graphed relationship proportional? Explain using the straight-line and origin test.
Check both conditions: straight line and through the origin.
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Is the graphed relationship proportional? Explain using the straight-line and origin test.
Check both conditions: straight line and through the origin.
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Is the graphed relationship proportional? Explain using the straight-line and origin test.
Check both conditions: straight line and through the origin.
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Is the graphed relationship proportional? Explain using the straight-line and origin test.
Check both conditions: straight line and through the origin.
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Is the graphed relationship proportional? Explain using the straight-line and origin test.
Check both conditions: straight line and through the origin.
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Is the graphed relationship proportional? Explain using the straight-line and origin test.
Check both conditions: straight line and through the origin.
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Is the graphed relationship proportional? Explain using the straight-line and origin test.
Check both conditions: straight line and through the origin.
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Is the graphed relationship proportional? Explain using the straight-line and origin test.
Check both conditions: straight line and through the origin.
Exact-construction rule: fraction unit rates stay rational, graph coordinates come from known equations, and money applications use integer cents. No answer key depends on a hidden rounding convention.
How to tell if a graph shows a proportional relationship
The graph of a proportional relationship is a straight line that passes through the origin, (0, 0). Both conditions are required: a straight line that misses the origin, or a curve, is not proportional. You can also check by finding y ÷ x for several plotted points, which should always give the same number.
Worked examples
- Points (1, 3), (2, 6) and (3, 9) lie on a line through (0, 0), and y ÷ x is 3 each time, so it is proportional.
- Points (1, 4) and (2, 6) lie on a straight line, but the line crosses the y-axis at 2, not at the origin, so it is not proportional.
- A graph that curves, even if it starts at (0, 0), is not proportional.
Common slips
- Thinking any straight line is proportional. It must also pass through the origin.
- Checking only the origin. A line can pass through (0, 0) and still be a curve.
- Forgetting that y ÷ x must be the same for every point, not just two of them.
How to use this worksheet
Ask students to name both conditions (straight, through the origin) for every graph and to test one point with y ÷ x. The answer key states which graphs are proportional and why.
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 straight line is necessary but not sufficient; proportional graphs also pass through (0, 0).
Teacher tip 2
A positive y-intercept means there is already some y when x = 0, so the relationship is not y = kx.
Teacher tip 3
Example: y = 2x + 3 is a straight line but crosses the y-axis at 3, so it is not proportional; any nonzero y-intercept is the tell.
Teacher tip 4
Ask students to name both tests rather than answering from visual appearance alone.
Continue the 7.RP progression
Move to another Grade 7 representation or application
Common questions
Are non-proportional graphs always curved?
No. This generator deliberately includes straight lines with nonzero intercepts so students must check the origin.
Are the plotted coordinates exact?
Yes. Every point uses integer coordinates generated from a known rule.
Can a proportional relationship graph as a curve?
No. A proportional relationship is always a straight line through the origin. A curve means the rate between y and x is changing.