Linear Functions
Functions with a constant rate of change.
Key idea
Functions with a constant rate of change.
In depth
A linear function f(x) = mx + b has a constant rate of change m. Equal steps in x always create equal steps in y. It models steady growth such as a taxi fare or a savings plan.
Worked example
A plumber charges 40 plus 25 per hour: f(h) = 25h + 40. f(3) = 115.
Formula
Real-world uses
- Modelling steady growth such as a savings account with fixed deposits or a constant wage rise
Common mistake
Using linear models for situations that are not constant, such as population.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Linear Functions?
Functions with a constant rate of change. It is a topic at the intermediate level in Algebra.
What is the formula for Linear Functions?
The key formula is f(x) = mx + b.
Where is Linear Functions used in real life?
Real-world examples: Modelling steady growth such as a savings account with fixed deposits or a constant wage rise.
What should I learn before Linear Functions?
Make sure you are comfortable with Graphing Linear Equations, the previous topic in Algebra.
What is a common mistake with Linear Functions?
Using linear models for situations that are not constant, such as population.
How can I practise Linear Functions?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Linear Functions?
Move on to Function Notation next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.