Line (geometry)

There are many variant ways to write the equation of a line which can all be converted from one to another by algebraic manipulation. The above form is sometimes called the standard form. If the constant term is put on the left, the equation becomes

In three dimensions lines are frequently described by parametric equations:

Parametric equations for lines in higher dimensions are similar in that they are based on the specification of one point on the line and a direction vector.

As a note, lines in three dimensions may also be described as the simultaneous solutions of two linear equations

A ray starting at point A is described by limiting λ. One ray is obtained if λ ≥ 0, and the opposite ray comes from λ ≤ 0.

However, there are other notions of distance (such as the Manhattan distance) for which this property is not true.