Linear equations and graphs.
Connect equations, coordinate geometry and straight-line models through clearly explained methods, original diagrams and progressive practice.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Equation-solving consolidation
Solve equations by preserving equality, then check the answer in the original statement.
- 02
Gradient as rise/run
Measure the steepness and direction of a line using vertical change divided by horizontal change.
- 03
Midpoint
Find the halfway point of a segment by averaging its two coordinates separately.
- 04
Distance between points using Pythagoras
Use horizontal and vertical differences as the legs of a right triangle to calculate a straight-line distance.
- 05
Straight-line equations and intercepts
Connect the slope and axis crossings of a straight line with its algebraic rule.
- 06
Finding a line from information
Build a straight-line equation from a gradient, a point, or two coordinate points.
- 07
Parallel/perpendicular lines as a natural school extension
Use gradients to recognise parallel and perpendicular straight lines and construct examples through a point.
- 08
Interpreting linear models
Interpret the gradient, intercept and valid input values of a linear model, then use it carefully in a context.
- 09
Testing parameter changes digitally
Test how changing a line's gradient or intercept affects its graph, using controlled comparisons and supplied values.
Topic review
Revisit the key ideas, then choose a practice paper.