It was independently discovered by Pierre de Fermat, who also worked in three dimensions, although Fermat did not publish the discovery..Both Descartes and Fermat used a single axis in their treatments and have a variable length measured in reference to this axis.A plane with x- and y-axes defined is often referred to as the Cartesian plane or xy-plane.
Every real number has a unique location on the line.
Conversely, every point on the line can be interpreted as a number in an ordered continuum such as the real numbers.
Then each point P of the line can be specified by its distance from O, taken with a or − sign depending on which half-line contains P.
A line with a chosen Cartesian system is called a number line.
Choosing a Cartesian coordinate system for a one-dimensional space – that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line.