IGCSEMathsCambridge (CIE)ExtendedRevision NotesCoordinate Geometry & GraphsLinear GraphsParallel Lines

Parallel Lines (Cambridge (CIE) IGCSE Maths)

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Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Parallel Lines

What are parallel lines?

Parallel lines are straight lines with the same gradient
- Two parallel lines will never meet
  - They just stay side-by-side forever
The equation of the line parallel to y = mx + c is y = mx + d
- $y = 2 x + 1$ and $y = 2 x + 5$ are parallel
- $y = 2 x + 1$ and $y = 3 x + 1$ are not parallel

How do I find the equation of a parallel line?

For example, to find the equation of the line parallel to y = 2x + 1 which passes through the point (3, 14)
- write the parallel line as y = 2x + d
  - using the same gradient of 2
- substitute x = 3 and y = 14 into this equation
  - 14 = 2 × 3 + d
  - 14 = 6 + d
- solve to find d
  - d = 8
- The equation is y = 2x + 8

Worked Example

Find the equation of the line that passes through the point (2, 1), which is parallel to the straight line $y = 3 x + 7$ .

Parallel means the gradient will be the same
Use y = mx + d where m = 3

$y = 3 x + d$

Substitute in x = 2 and y = 1

$1 = 3 \times 2 + d$

Simplify the equation

$1 = 6 + d$

Solve the equation to find d (by subtracting 6 from both sides)

$- 5 = d$

Write out the final answer in the form y = mx + d

$y = 3 x - 5$

Last updated: 24 May 2024

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Mark Curtis

Author: Mark Curtis

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.