Editing Line (geometry) (section)

=== Parametric equation ===
{{Further|Parametric equation}}
Parametric equations are also used to specify lines, particularly in those in [[Three-dimensional space|three dimensions]] or more because in more than two dimensions lines ''cannot'' be described by a single linear equation.

In three dimensions lines are frequently described by parametric equations:
<math display="block">\begin{align}
x &= x_0 + at \\
y &= y_0 + bt \\
z &= z_0 + ct
\end{align}</math>
where:
* ''x'', ''y'', and ''z'' are all functions of the independent variable ''t'' which ranges over the real numbers.
* (''x''<sub>0</sub>, ''y''<sub>0</sub>, ''z''<sub>0</sub>) is any point on the line.
* ''a'', ''b'', and ''c'' are related to the slope of the line, such that the direction [[vector (geometric)|vector]] (''a'', ''b'', ''c'') is parallel to the line.

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.