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Equation of a line

Free Printable Equation of a line PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free equation of a line worksheets (PDF), GCSE maths past paper questions and worked solutions for Equation of a line (5R). This is a Grade 5 algebra topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Dr Frost, Maths4EveryOne, 1st Class Maths, Dr Austin, Metatutor, IGCSE MT, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our equation of a line revision notes and worked examples with diagrams, try real GCSE past paper equation of a line questions with step-by-step solutions, or download a PDF of all equation of a line worksheet links.

Free Equation of a line PDF Worksheets & Answers

Grade 5 • Topic 5R
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Grade 5 topics
5A - Combining ratios5B - Direct and inverse proportion
5C - Reverse percentages5D - Standard form
5E - Speed5F - Changing the subject
5G - Quadratic expressions5H - Solving quadratic equations
5J - Drawing quadratic graphs5K - Cubic/reciprocal graphs
5L - Simultaneous equations5M - Sector areas and arc lengths
5N - Sim. equ. graphically5P - Midpoint of a line segment
5Q - Gradient of a line5R - Equation of a line
5S - Spheres and cones5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)5V - Exact trig. values
5W - Probability trees5X - Vectors
5Y - Venn diagrams5Z - Density
5AA - Pressure
GCSE Maths Grade 5 Revision Notes & Method

Guide to Equation of a line: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

The equation of a straight line is written in the form y = mx + c, where m is the gradient and c is the y-intercept (the value of y where the line crosses the y-axis at (0, c)).

To find the equation of a line from two points, first calculate the gradient m = y2 − y1x2 − x1, then substitute m and the coordinates (x, y) of one point into y = mx + c to find c.

Example 1: Find the equation of the line with gradient 4 that passes through the point (2, 5).

Solution:

Start with y = 4x + c
Sub (2, 5): 5 = 4(2) + c
5 = 8 + c → c = −3
Answer: y = 4x − 3
(0,−3) (2,5) m = 4

Example 2: Find the equation of the line passing through (−2, 7) and (4, −5).

Solution:

Gradient m = −5 − 74 − (−2) = −126 = −2
Substitute m = −2 and (4, −5) into y = mx + c:
−5 = −2(4) + c → −5 = −8 + c → c = 3
Answer: y = −2x + 3
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Equation of a line Questions & Answers

Past Paper Example 1 OCR Nov 2023 2F Q24 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
A straight line passes through the points (0, 5) and (2, 13).
xyO5132Not to scale
Find the equation of the line in the form y = mx + c.
Worked Solution & Mark Scheme (4 marks)
Gradient m = (13 − 5) ÷ (2 − 0) = 8 ÷ 2 = 4. M2
y-intercept c = 5. M1
Equation of line: y = 4x + 5. A1
Answer: y = y = 4x + 5
Past Paper Example 2 GCSE May 2025 1F Q25 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
The straight line **L** is shown on the grid.
12341234xyOL
Find an equation for **L**.
Give your answer in the form y = mx + c
Worked Solution & Mark Scheme (3 marks)
y-intercept c = 3. Gradient m = (0 – 3) ÷ (4 – 0) = –3/4 = –0.75 M2
Equation: y = –3/4 x + 3. A1
Answer: y = -34x + 3
Past Paper Example 3 IGCSE Jun 2023 1H Q13 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
Work out
A is the point with coordinates (-5, 12)
B is the point with coordinates (19, -48)
Find an equation of the straight line that passes through the points A and B
Worked Solution & Mark Scheme (3 marks)
Gradient m = (–48 – 12) ÷ (19 – –5) = –60 ÷ 24 = –2.5. Using (–5, 12): 12 = –2.5(–5) + c => 12 = 12.5 + c => c = –0.5. Equation: y = –2.5x – 0.5 (or 5x + 2y + 1 = 0). M2 A1
Answer: y = y = -2.5x - 0.5

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