Linear equations and graphs — Topic Review | Year 9

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.

Complete each paper and show your working.

Linear equations and graphs — practice paper 1
16 questions · 45 marks · 55 minutes · By hand
Build from equations and coordinate facts to straight-line rules, geometric reasoning and contextual models.
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Linear equations and graphs — practice paper 2
16 questions · 47 marks · 55 minutes · By hand
Build from equations and coordinate facts to straight-line rules, geometric reasoning and contextual models.
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Linear equations and graphs — applications paper
16 questions · 53 marks · 60 minutes · By hand
Use linear relationships, coordinate geometry and model checks in connected practical situations.
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