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Edexcel IGCSE Maths (4MA1) · Unit 4: Graphs & Functions

IGCSE Maths Straight Line Graphs Questions and Answers

Straight Line Graphs questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 5 worked examples first, then cover each solution and redo it yourself.

Practise straight line graphs in Unit 4 →Straight Line Graphs revision notes

What this topic covers

Straight Line Graphs worked examples

Worked example 1: Line through two points

Find the equation of the line through \((1,\ 3)\) and \((5,\ 11)\).

Solution

  1. Gradient \(=\dfrac{11-3}{5-1}=\dfrac{8}{4}=2\).
  2. Use \(y=2x+c\) with \((1,\ 3)\): \(3=2+c\), so \(c=1\).
  3. Equation: \(y=2x+1\).

Answer: \(y=2x+1\)

Tip: Check with the other point: 2 × 5 + 1 = 11.

Worked example 2: Midpoint

Find the midpoint of \((-3,\ 4)\) and \((7,\ -2)\).

Solution

  1. Average the x-coordinates: \((-3+7)\div2=2\).
  2. Average the y-coordinates: \((4+(-2))\div2=1\).

Answer: \((2,\ 1)\)

Tip: The midpoint is the mean of the coordinates.

Worked example 3: Table of values for a line

Find the points on \(y=2x-3\) for \(x=0,\ 1,\ 2\).

Solution

  1. \(x=0\): \(y=-3\).
  2. \(x=1\): \(y=-1\).
  3. \(x=2\): \(y=1\).

Answer: \((0,-3),\ (1,-1),\ (2,1)\)

Tip: Plot at least three points; a third point checks the other two.

Worked example 4: Gradient and intercept

Find the gradient and y-intercept of \(3y-6x=9\).

Solution

  1. Rearrange to \(y=mx+c\): \(3y=6x+9\).
  2. \(y=2x+3\): gradient 2, y-intercept 3.

Answer: Gradient 2, intercept 3

Tip: Always make y the subject first.

Worked example 5: Perpendicular line

Find the equation of the line perpendicular to \(y=-2x+5\) through \((4,\ 1)\).

Solution

  1. Perpendicular gradient: \(-1\div-2=\tfrac{1}{2}\).
  2. \(1=\tfrac{1}{2}\times4+c\), so \(c=-1\).
  3. \(y=\tfrac{1}{2}x-1\).

Answer: \(y=\tfrac{1}{2}x-1\)

Tip: Perpendicular gradients multiply to −1.

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise straight line graphs for the exam

Questions students ask

Which Edexcel IGCSE Maths papers test straight line graphs?

Either Higher tier paper, 1H or 2H, can test straight line graphs: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more straight line graphs questions?

In the IGCSE student hub: Unit 4 (Graphs & Functions) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 4 topics: Graphs & Functions