Year 8 Mathematics · AC9M8A02

Linear Relations, Equations and Inequalities

Connect tables, graphs and algebra as representations of the same linear relationship. Solve equations and inequalities by preserving equality or order, then verify…

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Key conceptTeach from the board

A relation is linear when equal changes in the independent variable produce constant changes in the dependent variable. In a table this appears as constant first differences; on a graph the points lie on a straight line.

An equation asks for values that make two expressions equal. An inequality such as 2x+1<9 describes a set of values, not one isolated answer. The Year 8 Australian descriptor explicitly connects graphical and algebraic solution methods and substitution checks.

For two expressions, the equation solution is the x-coordinate where their graphs intersect. Algebra, graph and substitution should agree.

Worked examplesWe do

Worked examples

AC9M8A02 - Linear Relations, Equations and Inequalities
Example 1

Complete a table for y=3x+2 and identify the first difference.

Example 2

Plot three points for y=−x+4 and explain why the graph is linear.

Example 3

Solve 4x−5=19 and verify by substitution.

Example 4

Solve 3x+2<14 and represent the solution on a number line.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8A02: graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8A02:Exact relationship.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-EQU-C-01; MA4-LIN-C-01; MAO-WM-01:Partial. NSW Stage 4 covers equations and graphical linear relationships, but AC9M8A02 is broader because it explicitly includes one-variable inequalities and the full graph–algebra verification sequence.

LessonAC v9VictoriaNSW
Linear relations, equations and inequalitiesAC9M8A02VC2M8A02 — ExactMA4-EQU-C-01; MA4-LIN-C-01; MAO-WM-01 — Partial
Questions and answersWith answers
  1. How can a table indicate linearity? Constant first differences for equally spaced x-values show constant rate of change.
  2. What does solving an equation mean? Finding value(s) that make the two sides equal.
  3. Why is an inequality answer often a range? Many values can satisfy a comparison.
  4. How can a graph verify a solution? The algebraic solution matches an intersection or boundary; substitution confirms it numerically.
Practice and reviewReady for practice
  • A linear graph must pass through the origin. Only zero-intercept relations do.
  • An inequality has one answer. It usually represents an interval or set.
  • Solving means changing one side only. Equality is preserved by equivalent operations on both sides.
  • A graph is decorative. Straightness, intersections, boundaries and regions are mathematical evidence.
Curriculum alignmentStart here
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