DfE statement A9 · Algebra

Straight-line graphs and y = mx + c

part HigherNon-calculator

Straight-line graphs and y = mx + c is content statement A9 of the DfE GCSE mathematics subject content, in the algebra area. It is on both tiers, with a Higher-only part, and it is examined without a calculator. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel and perpendicular lines; find the equation of the line through two given points, or through one point with a given gradient." (statement A9). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement A9

Tier

Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "and perpendicular lines". Everything else in the statement is Foundation content.

Calculator

This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.

Common mistakes

Calculating the gradient as run over rise instead of rise over run.
Taking the perpendicular gradient as −m rather than −1/m. The product of perpendicular gradients is −1.
Reading c off the graph where the line crosses the vertical grid edge rather than where it crosses the y-axis, when the axes do not start at zero.

Sample questions (10 of 30)

A9 · Straight-line graphs and y = mx + cQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Algebra

Advanced

A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

y = -4x + 1

💡 Hints:

Foundation worksheet Higher worksheet Foundation algebra practice Higher algebra practice

Nearby statements

A1Algebraic notation A2Substitution into formulae A3Expressions, equations, formulae, identities and inequalities A4Simplifying, expanding and factorisingpart Higher A5Rearranging formulae A6Identities, equivalence and algebraic proofpart Higher A7Functions, inverse and composite functionspart Higher A8Coordinates in all four quadrants A10Gradients and intercepts of linear functions A11Roots, intercepts and turning points of quadraticspart Higher A12Recognising and sketching graphspart Higher A13Translations and reflections of graphsHigher only A14Real-life graphs and kinematicspart Higher A15Gradients and areas under graphsHigher only A16Equation of a circle and its tangentHigher only A17Linear equations A18Solving quadratic equationspart Higher A19Simultaneous equationspart Higher A20IterationHigher only A21Forming and solving equations from situations A22Linear and quadratic inequalitiespart Higher A23Generating sequences A24Special sequences: square, cube, Fibonacci, quadratic, geometricpart Higher

Questions people ask

Is straight-line graphs and y = mx + c on Foundation or Higher?

Both, but not all of it. The parts the DfE prints in bold — "and perpendicular lines" — are Higher only; the rest is Foundation content.

Can I use a calculator for straight-line graphs and y = mx + c?

Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.

What is the single most common mistake here?

Calculating the gradient as run over rise instead of rise over run.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

Back to Algebra at Foundation or at Higher.