Linear Relationships
Straight-line relationships, gradients, intercepts, direct variation, practical linear models and graph interpretation.
Active lessons
8
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
8 of 8 active
Lesson 1
Linear Relationships and Graphs
Interpret straight-line rules, tables and graphs using gradients, rates and starting values.
Lesson 2
Direct Variation and Practical Linear Models
Use direct variation, constants of variation and practical linear models with and without fixed costs.
Lesson 3
Constructing Linear Models
Write a linear rule from a word description, two given points or a table of values, and verify by substituting back.
Lesson 4
Piecewise and Step Functions
Identify and evaluate piecewise and step models with different rates for different input ranges, such as tariffs and parking fees.
Lesson 5
Break-even Analysis
Find the break-even quantity by setting revenue equal to cost and interpret profit and loss regions in practical contexts.
Lesson 6
Practical Limitations of Linear Models
Identify domain restrictions, explain why extrapolation may be unreliable, and state meaningful limitations of linear models in context.
Lesson 7
Linear Relationships Exam Practice
Practise mixed linear relationship questions using tables, rules, graph features, direct variation and practical limitations.
Lesson 8
Linear Relationships Revision
Activate Year 10 prior knowledge: plotting points on the Cartesian plane, identifying gradient, reading and interpreting straight-line graphs, and completing tables of values.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.