A line is a straight one-dimensional geometric object. In applied geometry, coordinates and equations turn that intuition into a form suitable for programming, modeling, and computation. section 2.3 section 1.2
In two dimensions, the explicit equation y = ax + b constructs a line as a function graph, but it cannot represent a vertical line. The general implicit form handles vertical lines as well; a canonical form adds a point and direction coefficients. section 2.3.1
Three-dimensional lines require a different representation. Adding a scaled z variable to a two-dimensional general equation produces a plane, so a 3D line is described by a pair of equations, equivalently as the intersection of two nonparallel planes. section 2.3.1
Constant-speed motion
A 2D game trajectory can be assembled from line and circular-arc segments. Moving through a line’s parametric form at a constant parameter rate produces constant-speed motion; equal parameter increments similarly give proportional progress around a circle. section 5.3
