Line

A line was described by Euclid as having "breadthless length." This means that a line in infinitely long, but has no width. Lines can be considered as curves with infinite radius of curvature. A line that can be drawn on paper is not actually a line, but a representation of a line. Two points determine a line. A line can be broken down into finite line segments.

Common mathematical representations of a line include:

In 2 dimensions:

• Standard Form: ax + by + c = 0
• Slope-Intercept Form: y = mx + b (where m is the slope of the line, b is the y-intercept)
• Point-Slope Form: (y - y₀) = m(x - x₀) (where m is the slope and (x₀, y₀) is a point on the line)

In n dimensions:

• Parametrized Vector Form: r(t) = <x₀, y₀,...> + t<x, y,...>