Year 8 Mathematics · AC9M8A04

Experimenting with Linear Functions and Relations

Run controlled mathematical experiments: vary one feature at a time, predict what will happen, use digital tables and graphs to test the conjecture, then state a…

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Key conceptTeach from the board

A useful digital experiment controls variables. In y=mx+b, hold b fixed while changing m to isolate the effect of gradient; hold m fixed while changing b to isolate the intercept effect.

The conjecture must be stated before or during testing, then challenged with positive, zero and negative cases where relevant. One attractive graph is not proof of a general rule.

Digital tools accelerate variation and comparison, but reasoning remains mathematical: identify what changed, what stayed invariant and whether the evidence supports the claimed generalisation.

Victoria numbering note: this national descriptor AC9M8A04 aligns to Victorian VC2M8A05. Victorian VC2M8A04 is a separate algorithms/testing-and-error-correction descriptor, so matching by number alone would be incorrect.
Worked examplesWe do

Worked examples

AC9M8A04 - Experimenting with Linear Functions and Relations
Example 1

Graph y=2x+b for b=−3,0,4 and state what remains invariant.

Example 2

Graph y=mx+1 for m=−2,0,3 and describe the effect of m.

Example 3

Test which side of y=x+2 satisfies y>x+2.

Example 4

List three integer solutions to x+2y=8.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8A04: experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8A05:Exact relationship. Victoria inserts a separate algorithms/error-correction descriptor at VC2M8A04, so the equivalent linear-functions descriptor is VC2M8A05.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-LIN-C-01; MAO-WM-01:Partial. NSW supports creating/displaying linear relationships and Working Mathematically, but does not reproduce the full national systematic digital experimentation descriptor as a single Stage 4 outcome.

LessonAC v9VictoriaNSW
Experimenting with linear functionsAC9M8A04VC2M8A05 — ExactMA4-LIN-C-01; MAO-WM-01 — Partial
Questions and answersWith answers
  1. Why vary one parameter at a time? To isolate its effect rather than mixing causes.
  2. What happens when b changes with m fixed? The line shifts vertically and remains parallel.
  3. What does negative m do? The line decreases from left to right.
  4. What makes a conjecture convincing? It survives systematic tests, including relevant boundary or contrasting cases.
Practice and reviewReady for practice
  • One graph proves a general rule. Test multiple strategically different cases.
  • Changing b changes gradient. In y=mx+b, b shifts the line vertically but does not change m.
  • Digital tools replace explanation. They provide evidence; the conjecture and generalisation require reasoning.
  • A visual intersection is automatically exact. Readings may be approximate; verify algebraically when exactness matters.
Curriculum alignmentStart here
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