Linear functions, graphs and equations

Linear functions are fundamental building blocks in mathematics and play a key role in solving real-world problems where the rate of change remains constant. Linear functions arise in a wide range of applications because they often capture the essential relationships without becoming overly complicated. They span various fields, including economics, where they model supply and demand, physics, to describe motion and forces, and data analysis, for interpreting trends and making predictions.  They provide a versatile framework for solving equations, visualising data, and making informed decisions.

This resource revises linear functions, graphs and equations and within linear functions, graphs and equations there are 3 key concepts:

To determine if this resource will benefit you, start by answering the following questions.

  • Have you ever encountered a situation where you needed to compare two options or predict outcomes based on trends? How might linear equations help with this?
  • What does it mean for a graph to have a constant rate of change, and how is this used to solve real-world problems?
  • What do the intercepts of a linear graph reveal about real-world relationships, and how can they be used to interpret starting points, limits, or key decision points in problem-solving?

The answers to these questions are provided on the following pages. Use this resource to refresh your memory, reinforce your understanding of these concepts, and prepare more effectively for university-level learning.