Identifying Proportional Relationships in Graphs (A) - Proportional Relationship Worksheets

Sep 23, 2026

Uploaded by Jacob

Practice for determining whether a graph represents a proportional relationship using two required conditions: the graph must be a straight line and must pass through the origin (0,0). Includes Part A questions where students check each graph for straightness and origin intersection, and Part B tasks where students evaluate proportionality from given point sets and sketch the corresponding graph. A challenge problem compares two students’ graphs, identifies proportionality, and derives the equation y = kx with an explanation of k.

LanguageEnglish

CategoryExam

FormatPDF

Pages5

Reading Time13 min

AccessFree to download

Part A: Graphs

Part B: Point Sets

Challenge Problem

Name: ______________________________________ Identifying Proportional Relationships in Graphs (A) Remember: A graph shows a proportional relationship when: (1) it is a straight line, AND (2) it passes through the origin (0, 0) . Both conditions must be true. If the line is straight but misses the origin: NOT proportional. If it passes through (0, 0) but curves: NOT proportional. Part A: For each graph, determine if the relationship is proportional. Explain using the two conditions: straight line AND through origin. 1.) Passes through (0, 0)? Straight line? Proportional? Explain: 2.) Passes through (0, 0)? Straight line? Proportional? Explain: 3.) Passes through (0, 0)? Straight line? Proportional? Explain: Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 4.) Passes through (0, 0)? Straight line? Proportional? Explain: 5.) Passes through (0, 0)? Straight line? Proportional? Explain: 6.) Passes through (0, 0)? Straight line? Proportional? Explain: Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) Part B: For each set of points on a graph, determine if the relationship is proportional. Explain using the two conditions: straight line AND through origin. Sketch the graph on the blank space provided. 7.) Points on the graph: (0, 1) (1, 3) (2, 5) (3, 7) Passes through (0, 0)? Straight line? Proportional? Explain: 8.) Points on the graph: (0, 0) (4, 3) (8, 6) (12, 9) Passes through (0, 0)? Straight line? Proportional? Explain: 9.) Points on the graph: (0, 0) (1, 5) (2, 10) (3, 15) Passes through (0, 0)? Straight line? Proportional? Explain: 10.) Points on the graph: (0, 2) (2, 6) (4, 10) (6, 14) Passes through (0, 0)? Straight line? Proportional? Explain: Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 11.) Points on the graph: (0, 0) (2, 7) (4, 14) (6, 21) Passes through (0, 0)? Straight line? Proportional? Explain: 12.) Points on the graph: (0, 0) (1, 3) (4, 12) (9, 27) Passes through (0, 0)? Straight line? Proportional? Explain: 13.) Challenge Problem Two students graph their data. • Mia’s graph passes through (0,0), (2,8), (4,16) • Jae’s graph passes through (0,3), (1,6), (2,9) a) Determine if each student’s graph shows a proportional relationship. Explain. b) For the proportional graph, find k and write the equation y = kx. c) What does k represent? Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) ANSWER KEY 1.) Origin: Yes | Straight: Yes | Proportional: Yes—Yes—straight line through origin, k=4 2.) Origin: No | Straight: Yes | Proportional: No—No—straight line but does not pass through (0,0) 3.) Origin: Yes | Straight: Yes | Proportional: Yes—Yes—straight line through origin, k=3/2 4.) Origin: No | Straight: Yes | Proportional: No—No—horizontal line, does not pass through origin 5.) Origin: Yes | Straight: No | Proportional: No—No—passes through origin but is not a straight line (curves) 6.) Origin: Yes | Straight: Yes | Proportional: Yes—Yes—straight line through origin, k=2/3 7.) Origin: No | Straight: Yes | Proportional: No—No—straight line but y-intercept = 1, not 0 8.) Origin: Yes | Straight: Yes | Proportional: Yes—Yes—straight line through origin, k=3/4 9.) Origin: Yes | Straight: Yes | Proportional: Yes—Yes—straight line through origin, k=5 10.) Origin: No | Straight: Yes | Proportional: No—No—straight line but does not pass

FAQs

What two conditions make a graph proportional?

A graph is proportional only if it is a straight line and it passes through the origin (0,0). Both conditions must be true.

If a graph is straight but does not pass through (0,0), is it proportional?

No. A straight line that misses the origin is not proportional because it fails the origin requirement.

For a proportional graph, how do you find the equation y = kx and what does k mean?

Identify the proportional constant k from the proportional graph or point set, then write y = kx. The value of k represents how many times the y-value is compared to the x-value.

Sep 23, 2026

Uploaded by Jacob

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