Year 8 Mathematics · AC9M8A03

Mathematical Modelling with Linear Relations

Build a linear model from a starting value and constant rate, choose a useful representation, interpret parameters in context and decide where the model stops being…

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Key conceptTeach from the board

A common linear model has the structure output = rate × input + starting value. The rate describes constant change; the starting value is the output when the input is zero, if zero is meaningful in the situation.

A modelling cycle is: formulate the question and assumptions → choose variables and representation → calculate → interpret with units → review whether the answer and model are reasonable.

The Australian descriptor includes financial contexts, pay rates, fares, motion, trade quotes and other applied situations. A correct equation is not enough: a model can become invalid outside its meaningful domain.

Worked examplesWe do

Worked examples

AC9M8A03 - Mathematical Modelling with Linear Relations
Example 1

Write a model for $8 entry plus $3 per ride.

Example 2

Interpret the rate and intercept in C=2.4d+6.

Example 3

Choose a table, graph or equation to compare two mobile plans and explain why.

Example 4

State one domain restriction for a tank-draining model.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8A03: use mathematical modelling to solve applied problems involving linear relations, including financial contexts; formulate, represent, interpret, communicate and review.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8A03:Exact relationship.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-LIN-C-01; MAO-WM-01:Partial. NSW supports linear relationships and mathematical reasoning, but does not mirror the full national modelling cycle and financial-context descriptor as one Stage 4 outcome.

LessonAC v9VictoriaNSW
Linear modellingAC9M8A03VC2M8A03 — ExactMA4-LIN-C-01; MAO-WM-01 — Partial
Questions and answersWith answers
  1. What does the coefficient represent? A constant rate of change per unit of input.
  2. What does the intercept represent? The initial/fixed output when input is zero, where meaningful.
  3. Why choose different representations? Equations support exact calculation, tables selected cases and graphs comparison/trends.
  4. When is a linear model inappropriate? When rate, assumptions or domain no longer match the real situation.
Practice and reviewReady for practice
  • The intercept is just a graph feature. In context it often represents a fixed or initial amount.
  • A straight-line rule can be extrapolated forever. Real constraints can limit its domain.
  • Units do not matter after calculation. Units are essential to interpretation.
  • A correct calculation proves the model is good. Assumptions and appropriateness must also be reviewed.
Curriculum alignmentStart here
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