Stage – 4, Linear Relationships

Module 3: Linear Relationships

This module introduces students to the concept of straight‑line graphs and how they represent relationships between two variables. It builds visual, analytical, and problem‑solving skills, showing how algebra and geometry connect in real‑world contexts.

1. Cartesian Plane & Coordinates

• Understanding the x‑axis and y‑axis as reference lines.

• Plotting points using ordered pairs (x,y).

• Recognising quadrants and symmetry.

• Outcome: Students can locate and represent data or solutions on a graph.

2. Plotting Linear Graphs

• Using tables of values to plot straight lines.

• Recognising that linear equations (e.g., y=2x+3) produce straight lines.

• Drawing graphs accurately with scales and labels.

• Outcome: Students connect algebraic equations to visual representations.

3. Gradient & Intercepts

• Gradient (slope): Understanding rise/run, positive vs. negative slopes.

• Y‑intercept: Where the line crosses the y‑axis.

• X‑intercept: Where the line crosses the x‑axis.

• Practice: Identify gradient and intercepts from equations like y=3x+2.

• Outcome: Students interpret how coefficients affect the steepness and position of a line.

4. Interpreting Linear Relationships in Real‑Life Contexts

• Applying linear graphs to everyday scenarios:

  • Cost vs. quantity (e.g., buying tickets).

  • Distance vs. time (speed problems).

  • Business models (profit vs. sales).

• Using graphs to predict outcomes and make decisions.

• Outcome: Students see linear relationships as tools for modelling and solving practical problems.

Learning Outcomes

By the end of this module, students will:

• Plot and interpret points on the Cartesian plane.

• Draw and analyse straight‑line graphs.

• Understand gradient and intercepts as key features of linear equations.

• Apply linear relationships to real‑world contexts, strengthening mathematical modelling skills.