Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · 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. 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 definition is part of the Coordinate Geometry chapter in Cambridge O Level Mathematics (Syllabus D).
Common mistakes with Parallel Lines
- “Parallel means the gradients are negative reciprocals.” Swapped Parallel lines have equal gradients. Perpendicular lines have negative reciprocal gradients. The swap is a costly one, because it produces a tidy-looking answer that is nevertheless a completely different line.
Questions students ask about Parallel Lines
Is a line parallel to itself?
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.