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Proportional Graphs

A 7th-grade math lesson on identifying proportional relationships from coordinate plane graphs using the two fundamental criteria: straight line and passing through the origin.

LLogan-Greene

Proportional Graphs

A 7th-grade math lesson on identifying proportional relationships from coordinate plane graphs using the two fundamental criteria: straight line and passing through the origin.

LLogan-Greene

Grade 7 Mathematics • Proportional Reasoning Unit Key • Page 1 of 2

B

Detailed Solutions: Questions 7–15

1 point for correct decision + valid reason.

Q7 YES

✓ Straight line  |  ✓ Through (0,0)

Straight line through origin with negative slope (\(k = -2\)).

Q8 NO

✗ Straight line  |  ✗ Through (0,0)

Bent piecewise line; has a corner and fails both rules.

Q9 NO

✗ Straight line  |  ✓ Through (0,0)

Discrete points form a steep curve, not a straight line.

Q10 YES

✓ Straight line  |  ✓ Through (0,0)

Collinear points align in a straight line passing through (0,0).

Q11 NO

✓ Straight line  |  ✗ Through (0,0)

Points form a line, but the line misses the origin (crosses at \(y=-1\)).

Q12 NO

✓ Straight line  |  ✗ Through (0,0)

Horizontal line \(y=2\); straight line that never touches (0,0).

Q13 YES

✓ Straight line  |  ✓ Through (0,0)

Reference line \(y=x\); straight line through (0,0) with unit rate \(k=1\).

Q14 NO

✓ Straight line  |  ✗ Through (0,0)

Vertical line \(x=2.5\); straight line that does not pass through (0,0).

Q15 NO

✗ Straight line  |  ✓ Through (0,0)

Random scatter of points; no straight line pattern exists.

C

Detective Challenge: Exemplar & Rubric

Worth 1 Point

Model Student Response:

"Jordan forgot Rule 2. A graph must also pass through the origin (0,0) to be proportional. Graph 2 is straight, but it crosses the y-axis above the origin at (0, 1.5), so it is not proportional."

Full Credit (1 pt):

Identifies that Jordan missed Rule 2 (passing through the origin/0,0) and mentions that being straight alone is not enough.

Partial/No Credit (0 pts):

Simply states "Jordan is wrong" without specifying the origin rule, or gives an unrelated reason.

Recommended Grading Scale:

15–16 pts: Exceeds / Mastered 12–14 pts: Proficient 9–11 pts: Approaching (Needs Rule 2 Review) < 9 pts: Needs Intensive Support

Grade 7 Mathematics • Proportional Relationships Teacher Resource Key • Page 2 of 2

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