Free Printable WorksheetMathGrade 8Math Curriculum8.EE.C.8a

8.72 Interpreting and Classifying Systems from Graphs Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.72 Interpreting and Classifying Systems from Graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.72 Interpreting and Classifying Systems from Graphs - Based on the graph, which statement correctly describes the number of solutions? (CCSS 8.EE.C.8a; CA 8.EE.C.8a; MA 8.EE.C.8a)

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 8.72 Interpreting and Classifying Systems from Graphs skill assessments:

Problem 1Difficulty: Hard

On the same coordinate plane, Line A passes through (-12, -16), (0, -6), and (12, 4). Line B is given by y + 6 = (5/6)x. When both are graphed together, which conclusion is true?

AThe system has two solutions because the lines cross twice.

BThe two lines never meet, so no ordered pair solves both equations.

CThere are infinitely many solutions because the two graphs overlap completely.

DThe lines intersect once at (-4, -28/3), so the system has one solution.

Solution & Explanation:Both relations simplify to the same line, y = (5/6)x - 6, so the graphs overlap completely and the system has infinitely many solutions.

Problem 2Difficulty: Hard

A classmate looks at the two relations and gives this conclusion. Relation I crosses the y-axis at 7 and falls 8 units for every 3 units to the right. Relation II passes through (0, 7) and (3, -1). The student says, "The system has no solution because the equations are written differently." Which option best evaluates the claim?

AThe claim is incorrect because both equations represent the same line, so there are infinitely many solutions.

BThe claim is correct because different forms always mean different lines.

CThe claim is partly correct because the system has no solution at the y-axis.

DThe claim is correct because two equations cannot have more than one solution.

Solution & Explanation:Both relations simplify to the same line, y = (-8/3)x + 7, so the graphs overlap completely and the system has infinitely many solutions.

Problem 3Difficulty: Hard

On the same coordinate plane, Line r has table values x: -12, 0, 12; y: -19, -5, 9. Line s is given by 14x - 12y = 60. What is the best classification of this system?

Aa system with exactly two solutions.

Ba consistent independent system with intersection (-4, -29/3).

Cno solution, so the system is inconsistent.

Da consistent dependent system because the lines overlap completely.

Solution & Explanation:Both relations simplify to the same line, y = (7/6)x - 5, so the graphs overlap completely and the system has infinitely many solutions.

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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.EE.C.8a (Primary standard selected for prompt fields: CCSS 8.EE.C.8a. Skill statement: Based on the graph, which statement correctly describes the number of solutions? Associated standards listed with this skill: CCSS 8.EE.C.8a; CA 8.EE.C.8a; MA 8.EE.C.8a. Use this embedded wording as the best available supporting standard description for this workflow.).