Parallel Lines (Edexcel GCSE Maths: Foundation)

Revision Note

Test yourself
Naomi C

Author

Naomi C

Last updated

Parallel Lines

What are parallel lines?

  • Parallel lines are lines that have the same gradient
  • Parallel lines do not intersect with each other
  • You can easily spot that two lines are parallel when they are written in the form y equals m x plus c,
    • They will have the same value of m (gradient)
      • y equals 3 x plus 7 and y equals 3 x minus 4 are parallel (and therefore will never intersect)
      • y equals 2 x plus 3 and y equals 3 x plus 3 are not parallel (and therefore must intersect)

How do I know if two lines are parallel to one another?

  • If you are given the equations of two lines, rearrange them into the form y equals m x plus c if they are not in it already
    • If the two lines have the same value for m, they are parallel 

How do I find the equation of a line that is parallel to another line?

  • You may be asked to find the equation of a line parallel to a line of the form y equals m x plus c
    • You will also be given some information about a point that the parallel line, y equals m x plus d passes through; open parentheses x subscript 1 space comma space y subscript 1 close parentheses
    • Substitute into the equation, y equals m x plus d, the value of m (this will be the same as for the original line) and the coordinates of the point through which it passes open parentheses x subscript 1 comma space y subscript 1 close parentheses
    • Solve the equation formed to find d
    • Write the equation of the parallel line substituting in the values of m and d

Worked example

Find the equation of the line that is parallel to y equals 3 x plus 7 and passes through the point (2,1).

As the gradient is the same, the line that is parallel will be in the form

y equals 3 x plus d

Substitute in the coordinates that the line passes through 

1 equals 3 open parentheses 2 close parentheses plus d

Simplify

1 equals 6 plus d

Subtract 6 from both sides

negative 5 equals d

Write the equation in the form y equals m x plus d, substituting in the values of m and d that you have found

bold italic y bold equals bold 3 bold italic x bold minus bold 5

You've read 0 of your 10 free revision notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Naomi C

Author: Naomi C

Expertise: Maths

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.