Free Printable WorksheetMathAlgebra IMath CurriculumF-BF.1a

ALG1.45 Build Linear Functions from Points, Slope, or Graphs Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.45 Build Linear Functions from Points, Slope, or Graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.45 Build Linear Functions from Points, Slope, or Graphs - Primary standard selected for prompt fields in this prompt cell: CCSS F-BF.1a. Skill statement in this prompt cell: Select the equation, inequality, expression, or function that represents a linear function given two points, a point and slope, or a graph; Select the representation that shows the same line in slope-intercept, point-slope, and standard forms. Associated standards listed with this skill in this prompt cell: CCSS: F-BF.1a; A-CED.2; F-IF.7a; TEKS: §111.39(c)(2)(E–G), (3)(C); VA SOL: A.F.1 c–f; FL B.E.S.T.: MA.912.AR.2.2–2.4; NY-NGLS: AI-F.IF.7a, AI-A.CED.2; CA CCSSM: F-BF.1a, F-IF.7a; MA 2017: HS.F-BF.1a; DoDEA CCRSM; NAEP: Algebra—functions; NCTM P2A: Practices 4, 6.. Use this prompt-provided wording as the supporting standard description for this workflow.

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 I

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 ALG1.45 Build Linear Functions from Points, Slope, or Graphs skill assessments:

Problem 1Difficulty: Mastery
Which option shows equivalent point-slope and standard forms for the line y = (1/3)x - 7?
Ay - 5 = (1/3)(x + 6) and x - 3y = -21
By + 5 = 3(x - 6) and 3x - y = 21
Cy + 7 = (1/3)(x - 6) and x + 3y = 21
Dy + 5 = (1/3)(x - 6) and x - 3y = 21
Solution & Explanation:For y = (1/3)x - 7, the point (6, -5) is on the line, so y + 5 = (1/3)(x - 6). Multiplying by 3 gives 3y = x - 21, or x - 3y = 21.
Problem 2Difficulty: Mastery
Use the graph shown. Which standard form equation represents the graphed line?
A2x + 3y = 24
B3x - 2y = 24
C2x - 3y = 24
D2x - 3y = -24
Solution & Explanation:The line passes through (0, -8) and (6, -4). The slope is 4/6 = 2/3, so y = (2/3)x - 8. Rearranging gives 2x - 3y = 24.
Problem 3Difficulty: Mastery
The input x increases by 4 while the output y decreases by 10. When x = 0, y = 6. Which function represents the relationship?
Ay = (5/2)x + 6
By = -(5/2)x + 6
Cy = -10x + 6
Dy = -(2/5)x + 6
Solution & Explanation:The slope is change in y over change in x: -10/4 = -5/2. The y-intercept is 6, so the function is y = -(5/2)x + 6.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this ALG1.45 Build Linear Functions from Points, Slope, or Graphs worksheet?

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QIs this ALG1.45 Build Linear Functions from Points, Slope, or Graphs worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard F-BF.1a (Primary standard selected for prompt fields in this prompt cell: CCSS F-BF.1a. Skill statement in this prompt cell: Select the equation, inequality, expression, or function that represents a linear function given two points, a point and slope, or a graph; Select the representation that shows the same line in slope-intercept, point-slope, and standard forms. Associated standards listed with this skill in this prompt cell: CCSS: F-BF.1a; A-CED.2; F-IF.7a; TEKS: §111.39(c)(2)(E–G), (3)(C); VA SOL: A.F.1 c–f; FL B.E.S.T.: MA.912.AR.2.2–2.4; NY-NGLS: AI-F.IF.7a, AI-A.CED.2; CA CCSSM: F-BF.1a, F-IF.7a; MA 2017: HS.F-BF.1a; DoDEA CCRSM; NAEP: Algebra—functions; NCTM P2A: Practices 4, 6.. Use this prompt-provided wording as the supporting standard description for this workflow.).

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