Linear equations and graphs.
Solve and check linear equations, then connect rules with tables, graphs, inequalities and practical models.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Multi-step equations
Undo several operations while keeping both sides of an equation equal.
- 02
Brackets and variables on both sides
Expand brackets and solve when the unknown appears on both sides.
- 03
Equations with rational solutions
Keep rational solutions exact and deal correctly with fractional expressions.
- 04
Substitution checks
Use both original sides to confirm or reject a proposed solution.
- 05
One-variable inequalities and number-line solutions
Describe solution sets with inequality signs and labelled number lines.
- 06
Tables and straight-line graphs
Connect a rule with a table, ordered pairs and a straight-line graph.
- 07
Horizontal/vertical lines
Distinguish constant-output horizontal lines from fixed-input vertical lines.
- 08
How coefficients change a graph
Describe how the multiplier and constant change a straight-line rule.
- 09
Graphical solutions and intersection checks
Read the common point of two graphs and check both coordinates in both rules.
- 10
Real-world linear models with digital exploration
Define variables, build linear models and test their realistic domains.
Topic review
Revisit the key ideas, then choose a practice paper.