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Gradient of a line

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

Download free gradient of a line worksheets (PDF), GCSE maths past paper questions and worked solutions for Gradient of a line (5Q). 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, Maths Made Easy, Dr Frost, Dr Austin, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

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

Free Gradient of a line PDF Worksheets & Answers

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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 Gradient of a line: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

The gradient (m) of a straight line measures how steep it is: Gradient = Change in yChange in x = y2 − y1x2 − x1.

Lines sloping upwards from left to right have a positive gradient; lines sloping downwards from left to right have a negative gradient; horizontal lines have gradient 0. Always subtract the coordinates in the same order on top and bottom.

Example 1: Find the gradient of the line passing through A(2, 3) and B(6, 15).

Solution:

Use m = y2 − y1x2 − x1:
m = 15 − 36 − 2 = 124 = 3
Answer: Gradient = 3
A(2,3) B(6,15) Run = 4 Rise = 12

Example 2: Work out the gradient of the line joining P(−3, 7) and Q(5, 3).

Solution:

m = 3 − 75 − (−3) = −48
Simplify the fraction: m = −12 (or −0.5)
Answer: Gradient = −12
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Gradient of a line Questions & Answers

Past Paper Example 1 Practice Set 5 3F Q16 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
(a) On the grid, draw the line x = 3 [1 mark]
xy–4–3–2–11234–4–3–2–11234O
(b) On this grid, draw the line y = x [1 mark]
xy–4–3–2–11234–4–3–2–11234O
(c) Find the gradient of the straight line drawn on this grid. [2 marks]
xy–4–3–2–11234–3–2–11234567O
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Vertical line at x = 3
xy–4–3–2–11234–4–3–2–11234O
Answer (a): Vertical line at x = 3
Part (b) Solution:
Diagonal line through (–4, –4) and (4, 4)
xy–4–3–2–11234–4–3–2–11234O
Answer (b): Diagonal line through (–4, –4) and (4, 4)
Part (c) Solution:
(Gradient = change in y ÷ change in x) M1
Gradient m = change in ychange in x = y2 - y1x2 - x1
Answer: 1.5 A1
Answer (c): 1.5
Past Paper Example 2 Eduqas Nov 2018 1F Q19 5 marks
Full Paper (PDF) • Mark Scheme (PDF)
The graph shows the cost of delivery for goods bought at a furniture shop.
01234567891051015202530354045Cost (£)Distance (miles)
(a) Ceri buys a sofa from this shop and has it delivered.
Ceri lives 4 miles from the shop.
How much does Ceri pay for the delivery? [1 mark]
(b) Tick the correct statement about the distance and cost.
- They are not in proportion.
- They are in inverse proportion.
- They are in direct proportion.
- They are in indirect proportion. [1 mark]
Find the gradient of the line and state what it represents in this context. [3 marks]
Worked Solution & Mark Scheme (5 marks)
Part (a) Solution:
Reading from graph at distance = 4 miles gives cost = £18. B1
Answer (a): £ £18
Part (b) Solution:
The graph is a straight line through the origin (0, 0). B1
Answer (b): They are in direct proportion.
Part Solution:
(Gradient = change in y ÷ change in x)
Gradient = 45 / 10 = 4.5. It represents the cost per mile (£4.50/mile). M2 A1
Answer : Gradient = 4.5; represents the cost per mile of delivery (£4.50 per mile).
Past Paper Example 3 OCR Nov 2022 2F Q17 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
A straight line, L, is shown below.
LhvNot to scale
(a) Write down the ratio v : h when the gradient of line L is 4. [1 mark]
(b) Find the gradient of line L as a fraction in its simplest form when v : h = 14 : 6. [2 marks]
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
Gradient = v / h = 4 ⇒ v : h = 4 : 1. B1
Answer (a): 4 : 1
Part (b) Solution:
(Gradient = change in y ÷ change in x)
Gradient = v / h = 14/6 = 7/3. M1 A1
Answer (b): 73

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