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A line is a one-dimensional object that exists in one dimension or higher. A line has infinite length, zero width, and zero height. Two (or more) points define a line. The following equation gives a non-vertical line in two-dimensions where m is the slope (gradient) of the line, b is the y-intercept of the line, and x is the independent variable of the function y = f(x).

y = m x + b

In two dimensions, the following equation describes every line L (including vertical lines), where a, b, and c are real coefficients. Note that the line is vertical when b is zero, and the line is horizontal when a is zero.

a x + b y = c, where a and b are not both zero

In three dimensions, a line is given by the following two linear equations, where (a1, b1, c1) and (a2, b2, c2) are not proportional. This follows since a single linear equation describes a plane and two distinct planes intersect at a line.

a1 x + b1 y + c1 zd1 = 0
a2 x + b2 y + c2 zd2 = 0
Bins in Two Dimensions
  1. Line by Coefficients in 2D
  2. Line by Slope and Intercept in 2D
  3. Line by Slope and Point in 2D
  4. Line by Two Intercepts in 2D
  5. Line by Two Points in 2D