Free Printable WorksheetMathGrade 8Math Curriculum8.F.A.3

8.46 Distinguishing Proportional and Nonproportional Linear Relationships Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.46 Distinguishing Proportional and Nonproportional Linear Relationships. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.46 Distinguishing Proportional and Nonproportional Linear Relationships - Which graph or equation represents a proportional relationship (b = 0) versus a nonproportional linear relationship (b ≠ 0)? (CCSS 8.F.A.3; CA 8.F.A.3; MA 8.F.A.3)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 8.46 Distinguishing Proportional and Nonproportional Linear Relationships skill assessments:

Problem 1Difficulty: Hard
A line passes through the points (2,11) and (6,27). Which explanation is correct?
AProportional, because the slope is 4.
BProportional, because the points increase by the same amount.
CNonproportional, because the equation is y = 4x + 3.
DNonproportional, because the line is increasing.
Solution & Explanation:The slope is (27 - 11) / (6 - 2) = 4. Using point (2,11) gives 11 = 4(2) + 3, so the equation is y = 4x + 3 and the line is nonproportional.
Problem 2Difficulty: Hard
The equation 7x - y = 0 is given. Which explanation best describes the relationship?
ANonproportional, because x and y are on opposite sides of the equation.
BProportional, because rewriting gives y = 7x, so b = 0.
CNonproportional, because the slope is 7.
DProportional, because the x-coefficient is 7.
Solution & Explanation:Rewriting 7x - y = 0 gives y = 7x. Since the intercept is 0, the relationship is proportional.
Problem 3Difficulty: Hard
A line passes through (0,-5) and (4,7). Which explanation is best?
AProportional, because the slope is 3.
BProportional, because the graph is linear.
CNonproportional, because the y-intercept is -5 instead of 0.
DNonproportional, because the x-values are positive.
Solution & Explanation:The point (0,-5) shows the line crosses the y-axis at -5. Since the intercept is not 0, the relationship is nonproportional.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.F.A.3 (Primary standard selected for prompt fields: CCSS 8.F.A.3. Skill statement: Which graph or equation represents a proportional relationship (b = 0) versus a nonproportional linear relationship (b ≠ 0)? Associated standards listed with this skill: CCSS 8.F.A.3; CA 8.F.A.3; MA 8.F.A.3. Use this embedded wording as the best available supporting standard description for this workflow.).

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