Free Printable WorksheetMathAlgebra IIMath CurriculumA-REI.12

ALG2.59 Writing Inequalities from Graphs Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.59 Writing Inequalities from Graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.59 Writing Inequalities from Graphs - Identify inequality symbols and boundary types from shading and line style, and write the inequality that matches a graph. Associated source-listed standards: CCSS A-REI.12; CA CCSSM A-REI.12; MA 2017 A-REI.12; NY NGLS A-REI.12; TX TEKS Algebra II: §111.40.

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

Algebra II

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 ALG2.59 Writing Inequalities from Graphs skill assessments:

Problem 1Difficulty: Mastery

Consider a graph with a solid line through (0, 5) and (5, 6). The solution region is on the same side of the line from (0, 0). Which inequality is shown?

Ay <= -(1/5)x + 5

By >= (1/5)x + 5

Cy < (1/5)x + 5

Dy <= (1/5)x + 5

Solution & Explanation:The line through (0, 5) and (5, 6) is y = (1/5)x + 5. Point (0, 0) is below the boundary line. The shaded region is on the same side, so it is below the line. Because the boundary is solid, use an inclusive inequality. The graph represents y <= (1/5)x + 5.

Problem 2Difficulty: Mastery

A dashed boundary line passes through (0, 1) and (1, -3). The shaded region lies on the opposite side of the boundary from (1, 0). Which inequality matches the graph?

Ay <= -4x + 1

By < 4x + 1

Cy < -4x + 1

Dy > -4x + 1

Solution & Explanation:The line through (0, 1) and (1, -3) is y = -4x + 1. Point (1, 0) is above the boundary line. The shaded region is on the opposite side, so it is below the line. Because the boundary is dashed, use a strict inequality. The graph represents y < -4x + 1.

Problem 3Difficulty: Mastery

Consider a graph with a solid line through (0, -4) and (5, -1). The solution region is on the same side of the line from (5, 0). Which inequality is shown?

Ay <= (3/5)x - 4

By >= (3/5)x - 4

Cy > (3/5)x - 4

Dy >= -(3/5)x - 4

Solution & Explanation:The line through (0, -4) and (5, -1) is y = (3/5)x - 4. Point (5, 0) is above the boundary line. The shaded region is on the same side, so it is above the line. Because the boundary is solid, use an inclusive inequality. The graph represents y >= (3/5)x - 4.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard A-REI.12 (Identify inequality symbols and boundary types from shading and line style, and write the inequality that matches a graph. Associated source-listed standards: CCSS A-REI.12; CA CCSSM A-REI.12; MA 2017 A-REI.12; NY NGLS A-REI.12; TX TEKS Algebra II: §111.40.).