Cambridge O Level Additional Mathematics · Syllabus 4037 · Straight-Line Graphs
Parallel and Perpendicular Conditions
What is Parallel and Perpendicular Conditions?
Two distinct non-vertical lines are parallel when their gradients are equal, so that m1 = m2, and they are perpendicular when the product of their gradients is minus one, so that m1 m2 = -1, which is the same as saying each gradient is the negative reciprocal of the other. Both conditions require the gradients to exist, so neither applies to a vertical line. A horizontal line and a vertical line are perpendicular to each other, but this is established from the geometry rather than from the product rule, because a vertical line has no gradient to substitute. Two lines with equal gradients but different vertical intercepts are parallel and distinct; if the vertical intercepts match as well, the two equations describe one and the same line, which is not a parallel pair at all.
This definition is part of the Straight-Line Graphs chapter in Cambridge O Level Additional Mathematics.