Plotting Points on a Cartesian Plane
A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.
The Cartesian plane extends infinitely in all directions. To show this, math textbooks usually put arrows at the ends of the axes in their drawings.
The coordinates of a point in the plane are measured in relation to a "central" point, the origin: first to the right, then up. The coords are listed as (x, y) for (right, up). (Negative numbers are used for left and down.) In the picture, the origin is the blue dot. Three other points and their corresponding ordered pairs are shown.
The Cartesian plane is divided into four quadrants. These are numbered from I – IV, starting with the upper right and going around counterclockwise. (For some reason everybody uses roman numerals for this).
In Quadrant I, both the x– and y-coordinates are positive; in Quadrant II, the x-coordinate is negative, but the y-coordinate is positive; in Quadrant III both are negative; and in Quadrant IV x is positive but y is negative.
Points which lie on an axis (i.e., which have at least one coordinate equal to 0) are said not to be in any quadrant. Coordinates of the form (x, 0) lie on the horizontal x-axis, and coordinates of the form (0, y) lie on the vertical y-axis.
Coordinates are also used in writing equations for graphs; we can have a relation between x and y, and translate that into the language of pictures. If the relation (or equation) has infinitely many x and y pairs that make it true, then instead of single points, we get whole lines, curves, or regions.
In the first two examples, the functions are "linear" so the graphs are straight lines.
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The x and y coords add up to 2. 
The y is always twice the x. 
General function, at most one y per x.
More graphs and their equations are available in the functions and graphs section.
There are also other kinds of coordinate systems (see polar coordinates).
