Parallel & Perpendicular Lines (AQA GCSE Maths)

What are parallel lines?

• Parallel lines are lines that have the same gradient, but are not the same line
• Parallel lines do not intersect with each other
• You can easily spot that two lines are parallel when they are written in the form , as they will have the same value of  (gradient)
•  and are parallel (and therefore will never intersect)
•  and are not parallel (and therefore must intersect)
•  and  are not parallel; they are the exact same line

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

• As parallel lines have the same gradient, a line of the form  will be parallel to a line in the form , where  is the same for both lines
• If  then they would be the same line and therefore not parallel
• If you are asked to find the equation of a line parallel to , you will also be given some information about a point that the parallel line, passes through; 
• You can then substitute this point into and solve to find 

What are perpendicular lines?

• You should already know that parallel lines have equal gradients
• Perpendicular lines meet each other at right angles – ie they meet at 90°

What’s the deal with perpendicular gradients (and lines)?

• Before you start trying to work with perpendicular gradients and lines, make sure you understand how to find the equation of a straight line – that will help you do the sorts of questions you will meet
• Gradients m₁ and m₂ are perpendicular if m₁ × m₂ = −1
  • For example
    • 1 and −1
    • and 3
    • and 
• We can use m₂ = −1 ÷ m₁ to find a perpendicular gradient. This is called the negative reciprocal.

• If in doubt, SKETCH IT!