Graph Detective Worksheet
Grade 7 Math Ratios & Proportions
Graph Detective Worksheet
Name:
Date: Period:
The 2-Rule Proportional Test
A graph is proportional ONLY when BOTH rules pass!
1
Must be a STRAIGHT LINE
No curves, bends, corners, or zigzags.
2
Must pass through ORIGIN (0,0)
Must touch the center point (0,0).
PROPORTIONAL
Rule 1: Straight line? Yes
Rule 2: Crosses (0,0)? Yes
NOT PROPORTIONAL
Rule 1: Straight line? Yes
Rule 2: Crosses (0,0)? No (misses origin)
A
Practice: Questions 1–6
Check each rule box, decide YES or NO, and state why.
Question 1
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Reason:
Question 2
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Reason:
Question 3
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Reason:
Question 4
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Reason:
Question 5
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Reason:
Question 6
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Reason:
Quick Check: A graph with a corner, bend, or curve fails Rule 1!
Page 1 of 2
B
Practice: Questions 7–15
Check rules, circle YES or NO, and write why.
Question 7
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Why:
Question 8
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Why:
Question 9
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Why:
Question 10
Straight pattern?
Passes through (0,0)?
Proportional? YES / NO
Why:
Question 11
Straight pattern?
Passes through (0,0)?
Proportional? YES / NO
Why:
Question 12
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Why:
Question 13
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Why:
Question 14
Straight line?
Passes through (0,0)?
Proportional? YES / NO
Why:
Question 15
Straight pattern?
Passes through (0,0)?
Proportional? YES / NO
Why:
C
Detective Challenge: Spot the Error!
Jordan looked at Question 2 on Page 1 and claimed: "This graph is proportional because it is a completely straight line!"
Explain Jordan's error. Which rule did Jordan forget to check?
Scoring: _____ / 16 pts Self-Check: Did you test BOTH rules on every graph?
Page 2 of 2
Graph Detective Answer Key
Teacher Key Grade 7 Ratios & Proportions
Graph Detective Answer Key
Total: 16 Points
1 pt / question + 1 pt challenge
At-A-Glance Master Key (Questions 1–15)
Criteria: (1) Straight Line AND (2) Passes Through (0,0)
Q1: YES
Q2: NO
Q3: NO
Q4: YES
Q5: NO
Q6: NO
Q7: YES
Q8: NO
Q9: NO
Q10: YES
Q11: NO
Q12: NO
Q13: YES
Q14: NO
Q15: NO
A
Detailed Solutions: Questions 1–6
Verify both rules and student reasoning.
Question 1 YES
✓Straight line? YES
✓Passes through (0,0)? YES
Acceptable Reason: Straight line passing directly through (0,0); constant slope \(k = 0.5\).
Question 2 NO
✓Straight line? YES
✗Passes through (0,0)? NO
Acceptable Reason: Straight line, but fails Rule 2 because it crosses the y-axis at (0, 1.5), missing the origin.
Question 3 NO
✗Straight line? NO
✓Passes through (0,0)? YES
Acceptable Reason: Passes through (0,0), but fails Rule 1 because the graph is curved (non-linear).
Question 4 YES
✓Straight line? YES
✓Passes through (0,0)? YES
Acceptable Reason: Both rules pass: straight line that passes directly through the origin (0,0) with \(k = 2\).
Question 5 NO
✓Straight line? YES
✗Passes through (0,0)? NO
Acceptable Reason: Straight line, but fails Rule 2 because it crosses at (0, 2) and (4, 0), missing (0,0).
Question 6 NO
✗Straight line? NO
✓Passes through (0,0)? YES
Acceptable Reason: Touches (0,0), but fails Rule 1 because it bends into a V-shape (absolute value, not straight).
Teacher Pacing & Remediation Tip
Students testing below grade level frequently believe that any straight line is proportional. When reviewing Questions 2 and 5, prompt them: "Where does the line cross the y-axis? Put your finger on (0,0). Is the line touching your finger?" Reinforce that "linear" is not the same as "proportional."