01 / QUICK RECAP
Connect the ideas.
- Preserve equality by performing the same operation on both sides, then check the original equation.
- Calculate gradient as matching vertical change divided by horizontal change; vertical gradients are undefined.
- Average coordinates separately for a midpoint and use Pythagoras for a direct distance.
- In y = mx + c, m is the gradient and c is the vertical intercept.
- Substitute a known point to find an unknown intercept; parallel lines share a gradient and perpendicular non-horizontal gradients multiply to -1.
- Interpret units, input restrictions and assumptions before trusting a linear prediction.
- Investigate one parameter at a time and use substitution or counterexamples to explain graph behaviour.
02 / PRACTICE TESTS
Put it together.
Choose a paper and show your working.
Linear equations and graphs — practice paper 1
Build from equations and coordinate facts to straight-line rules, geometric reasoning and contextual models.
16 questions · 45 marks · 55 minutes · By handLinear equations and graphs — practice paper 2
Build from equations and coordinate facts to straight-line rules, geometric reasoning and contextual models.
16 questions · 47 marks · 55 minutes · By handLinear equations and graphs — applications paper
Use linear relationships, coordinate geometry and model checks in connected practical situations.
16 questions · 53 marks · 60 minutes · By hand
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Gradient, midpoint and distance; algebraic and graphical straight-line relationships; interpreting models and testing parameters. Parallel and perpendicular lines are included as a natural school-course extension. All explanations and questions are original.
Official curriculum source ↗