Cambridge IGCSE Mathematics · Syllabus 0580 · Coordinate Geometry
Parallel Lines
What is Parallel Lines?
Two distinct straight lines in the same plane that never meet, however far they are extended. For non-vertical lines this happens exactly when their gradients are equal, so a line parallel to y = mx + c has the same m but a different c, and finding a parallel line means copying the gradient and then using the given point to find the new intercept. Two vertical lines x = a and x = b are also parallel whenever a and b differ. Equal gradients together with equal intercepts do not describe two parallel lines: they describe the same line written twice. This requirement is worded identically for Core C3.6 and Extended E3.6.
This definition is part of the Coordinate Geometry chapter in Cambridge IGCSE Mathematics.
Common mistakes with Parallel Lines
- “Parallel lines have gradients that are related somehow.” Say it precisely Parallel lines have equal gradients. Nothing is done to the number at all: you copy it. If you find yourself doing arithmetic on a gradient while answering a parallel question, stop.
Questions students ask about Parallel Lines
Is a line parallel to itself? Core C3.6
No. Parallel lines are distinct lines that never meet, and a line meets itself everywhere. This matters when a question asks you to show two lines are parallel: equal gradients alone leave open the possibility that they are the same line, so a complete answer also shows the lines are different — usually by finding a point on one that is not on the other.