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WorksheetYear 9Level 3 · Challenge

Free Year 9 Gradient and Linear Equations Worksheet — Level 3

Find the gradient between two points, read the gradient and y-intercept from an equation, write the equation of a line and test whether a point lies on it. A challenge set for students ready to stretch further. This Year 9 worksheet has 10 questions and comes with a full answer sheet showing the working for every question.

Need more practice? Practice Set 2 · Practice Set 3 · Practice Set 4 — same skill, fresh questions, full answers.

Instant download · No sign-up · Free for personal, classroom and homeschool use

Year
Year 9
Subject
Maths
Topic
Linear Relationships & Graphs
Difficulty
Level 3 · Challenge
Estimated time
15 minutes
Curriculum
Australian Curriculum
Questions
10
Answers
Included, with working
Format
PDF (A4), print or complete online

Students will practise

  • finding the gradient between two points
  • reading the gradient and y-intercept from an equation
  • writing the equation of a straight line

Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.

What's next?

Completed: Year 9 Gradient and Linear Equations Worksheet — Level 3

  1. 1Year 9 Factorising and Solving Quadratics Worksheet — Level 1
  2. 2Year 9 Factorising and Solving Quadratics Worksheet — Level 2
  3. 3Year 9 Factorising and Solving Quadratics Worksheet — Level 3
← Easier: Level 2 · StandardStudy guide

How to use this worksheet

  1. Print the PDF or complete it on screen. Write the student's name and date at the top.
  2. Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
  3. Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
  4. Record the score, celebrate what went well, then follow the "What's next" suggestion.

Common questions

Who is this worksheet for?

Year 9 students (typically ages 14–15) working on linear relationships & graphs. It is pitched at level 3 · challenge; an easier version is linked above.

Are the answers included?

Yes. The PDF includes a full answer sheet with the working for every question. You can also view the answers online.

How long does it take?

About 15 minutes for 10 questions. Short, regular sessions work best: two or three a week beats one long one.

Do I need to sign up to download?

No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.

What should we do next?

Try Year 9 Factorising and Solving Quadratics Worksheet — Level 1.

Preview

Success TutoringWorksheetsYear 9 · Mathematics · Linear Relationships & Graphs

Year 9 Gradient and Linear Equations Worksheet — Level 3

Name

Date

Score /

Show your working. Gradient = rise ÷ run; the equation of a line can be written as y = (gradient)x + (y-intercept).

1.Does the point (−1, 4) lie on the line y = −2x + 4?
  1. AYes
  2. BNo
2.For the line y = x − 8, write the gradient and the y-intercept. (answer space)
3.A line has a gradient of −3 and passes through (−4, 21). Find its equation.
4.Does the point (−3, −15) lie on the line y = 4x − 5?
  1. AYes
  2. BNo
5.A line has a gradient of −5 and passes through (3, −14). Find its equation.
6.Does the point (−5, 31) lie on the line y = −5x + 6?
  1. AYes
  2. BNo
7.For the line y = −x − 1, write the gradient and the y-intercept. (answer space)
8.For the line y = −3x + 7, write the gradient and the y-intercept. (answer space)
9.A line has a gradient of 4 and passes through (−1, 0). Find its equation.
10.A line has a gradient of −3 and passes through (−3, 4). Find its equation.
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Preview — the PDF contains the full resource and answer sheet.

More Year 9 linear relationships & graphs resources

  • Study Guide

    Linear Graphs: Gradient and Intercept

    Explains the y = mx + c form of a straight line for Year 9: what the gradient and y-intercept mean, how to calculate the gradient from two…

    Difficulty
    Level 2 · Standard
    Time
    20 min
  • Worksheet

    Year 9 Gradient and Linear Equations Worksheet — Level 1

    Find the gradient between two points, read the gradient and y-intercept from an equation, write the equation of a line and test whether a…

    Difficulty
    Level 1 · Easier
    Time
    15 min
    Questions
    10 questions
    Answers
    Answers included
  • Worksheet

    Year 9 Gradient and Linear Equations Worksheet — Level 2

    Find the gradient between two points, read the gradient and y-intercept from an equation, write the equation of a line and test whether a…

    Difficulty
    Level 2 · Standard
    Time
    15 min
    Questions
    10 questions
    Answers
    Answers included

Linear Relationships & Graphs in other year levels

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About this resource

Created by
Success Tutoring Maths Team
Reviewed by
Success Tutoring
Last reviewed
1 October 2026
How it was made
Generated by checked procedures

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