ACARA Year 9 Mathematics (Age 14) — Overview, Topics & a Step-by-Step Lesson on Linear Relationships

Clear, student-friendly overview of ACARA Year 9 (age 14) maths topics with a step-by-step lesson on linear equations and graphing, practice problems and answers. Choose which topic you'd like next.

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Welcome — Year 9 (Age 14) ACARA Maths overview

Hi! I can teach any topic from the Australian Curriculum (ACARA) for Year 9. Below is a quick overview of common Year 9 topics, then a clear, step-by-step lesson on one key topic: linear relationships (solving linear equations and graphing).

Common ACARA Year 9 topics (short descriptions)

  • Number and Algebra: index laws, integers, rational/irrational numbers, recurring decimals, expanding and factorising algebraic expressions, solving linear and simple quadratic equations.
  • Linear relationships: writing equations of lines, converting to y = mx + c, plotting graphs, interpreting slope and intercept, solving pairs of linear simultaneous equations (graphical and algebraic).
  • Rates, ratios and percentages: percentage change, best buys, compound interest basics.
  • Measurement and geometry: Pythagoras' theorem, trigonometry in right triangles (sin, cos, tan), area and volume of 2D and 3D shapes, similarity and congruence.
  • Statistics and probability: collecting data, mean/median/mode, interpreting boxplots and scatterplots, correlation, chance experiments and probability rules.
  • Quadratics (intro): recognising parabolas, simple factorisation and solving by factorising.

Which topic would you like to study?

Tell me which one and I will give a step-by-step lesson. For now, here is a full lesson on Linear relationships — solving linear equations and graphing.

Lesson: Linear equations and graphs — step by step

Goal: Learn how to rearrange linear equations into y = mx + c, plot the graph, and interpret slope (m) and y-intercept (c).

Step 1 — Recognise a linear equation

A linear equation in x and y usually looks like ax + by = d (no x*y, no x2, etc.). Example: 2x + 3y = 12.

Step 2 — Rearrange to y = mx + c

We want y on its own. From 2x + 3y = 12, subtract 2x: 3y = 12 - 2x. Then divide by 3: y = (12/3) - (2/3)x = 4 - (2/3)x. It's conventional to write y = mx + c, so y = -(2/3)x + 4. Here m = -2/3 (slope), c = 4 (y-intercept).

Step 3 — Find two (or more) points to plot

To draw the line, find values of x and corresponding y. Two easy choices are:

  • Use the y-intercept: x = 0 => y = 4. So point (0, 4).
  • Choose another x, for instance x = 3. Then y = -(2/3)*3 + 4 = -2 + 4 = 2. So point (3, 2).
  • Optional: find x-intercept by setting y = 0: 0 = -(2/3)x + 4 => (2/3)x = 4 => x = 6. So point (6, 0).

Step 4 — Draw the graph

  1. Plot the points (0,4), (3,2) and (6,0) on a coordinate grid.
  2. Draw a straight line through the points — that is the graph of the equation.

Step 5 — Interpret slope and intercept

Slope m = -2/3 means for each increase of 3 in x, y decreases by 2. The y-intercept c = 4 is where the line crosses the y-axis (x = 0).

Worked example (complete)

Equation: 2x + 3y = 12

Step A: Rearrange: 3y = 12 - 2x → y = 4 - (2/3)x → y = -(2/3)x + 4.

Step B: Points: (0,4), (3,2), (6,0).

Step C: Plot and draw the line. Slope = -2/3, y-intercept = 4.

Practice problems (try them)

  1. Rearrange and graph: 4x - 2y = 8. (Find slope and intercept.)
  2. Rearrange and graph: 5x + 10y = 20. (Find slope and intercept.)
  3. Find the x-intercept of: 3x - 6y = 12.

Answers (check your work)

  1. 4x - 2y = 8 → -2y = 8 - 4x → y = -4 + 2x (or y = 2x - 4). Slope m = 2, intercept c = -4. (Points: (0,-4), (1,-2) etc.)
  2. 5x + 10y = 20 → 10y = 20 - 5x → y = 2 - (1/2)x (or y = -0.5x + 2). Slope m = -1/2, intercept c = 2. (Points: (0,2), (2,1) etc.)
  3. 3x - 6y = 12. For x-intercept set y = 0: 3x = 12 → x = 4. So x-intercept is (4,0).

Tips

  • Always rearrange to y = mx + c when you want to graph easily.
  • Plot the y-intercept first (x=0), then use the slope to move (rise over run).
  • Check by substituting a plotted point into the original equation.
  • If fractions appear, multiply to find integer points (choose x so y becomes integer) or use a calculator/graphing tool.

Which topic would you like next? I can teach any Year 9 ACARA topic step-by-step (Pythagoras, trig, factorising quadratics, statistics, probability, simultaneous equations, etc.). Tell me the one you want and I will give another lesson with examples and practice problems.

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