General Equation of a Line

Before construction, land surveyors map property boundaries using a digital coordinate system. Each boundary segment can be shown as a straight line.

These lines can have different orientations. Some slope upward or downward. Some are horizontal. Others are vertical.

To represent all of these lines in one standard way, surveying software can use the general equation of a line: A x plus B y plus C equals zero. Here, A, B, and C are constants, and A and B cannot both be zero.

When B is not zero, the equation can be rearranged into slope-intercept form, where the slope is negative A over B, and the y-intercept is negative C over B. In this form, when A equals zero, the slope becomes zero, giving the equation of a horizontal line.

But a vertical boundary line has an undefined slope, so it cannot be written in slope-intercept form. This is where the general equation works better. When B equals zero, the y-term disappears, and solving for x gives the equation of a vertical line.

So, the general equation gives the software one standard way to represent slanted, horizontal, and vertical property boundaries.