LinesA line, by definition, is a curve that geometrically is determined by two of its points. Our discussion here is on straight (linear) lines. A linear line is a onedimensional construct: it has length. As such, a linear line can exist in any coordinate system with one or more dimensions (we can probably interpret this to mean that a linear line can exist in any coordinate system, since a dimensionless coordinate system is nonexistent.) General Form of a Line
In plane geometry, a line is a set of points satisfying a linear equation of the form:
Standard Form/SlopeIntercept Form
A line with the equation:
A plot of the line \(y=3x+5\) shows the intercepts at (3,0) and (0,5).
Notes:
The angle between two lines with slopes \(m_1\) and \(m_2\) is:
Intercept Form of a Line
A line with an equation of the form:
PointSlope Form of a Line
A line with a slope \(m\) passing through a known point \((x_1,y_1)\) has the equation:
TwoPoint Form of a Line
A line passing through two known points \((x_1,y_1)\) and \((x_2,y_2)\) has an equation of the form:
Lines in SpaceGeneral Form of a Spacial Line
The general form of a line in space is given by the equation:
Symmetrical Form a Spacial Line (Standard Form)
The equation is written in terms of direction numbers {\(l,m,n\)} and a point on the line \((x_1,y_1,z_1)\):
TwoPoint Form of a Spacial Line
The equation is written in terms of two points on the line with coordinates \((x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\). It has the form:
Parametric Form of a Spacial Line
The line is descibed in terms of its direction cosines \(\{l,m,n\}\), a point on the line \((x_1,y_1,z_1)\), and a variable parameter \(d\),
which specifies the distance of the variable point \((x,y,z)\) from point \((x_1,y_1,z_1)\).


Analytic Geometry: Points  Analytic Geometry: Line Intersection 