Gradients, parallel and perpendicular lines

For two distinct points, m= y_2-y_1x_2-x_1 when x_2!= x_1. A vertical line is x=k and has undefined gradient. **Relationship** | **Condition** Parallel non-vertical lines | m_1=m_2 Perpendicular non-vertical lines | m_1m_2=-1 Horizontal and vertical lines | Perpendicular to each other The general form ax+by+d=0 includes vertical lines. For b 0, rearrange to y=- abx- db. Example Through (2,5) perpendicular to y=2x-1: m=- 12, so y-5=- 12(x-2), or x+2y-12=0.