Cartesian coordinate: An ordered set of numbers (x,y) that, in two-dimensional graphs, identifies how variables may be related graphically along a horizontal x-axis and a vertical y-axis.

______________________________________________________________________

Axis: One of the intersecting lines used to measure how variables are related in a Cartesian coordinate system. In a two-dimensional Cartesian coordinate system, the x-axis measures variables laid out horizontally and the y-axis measures variables laid out vertically. The plural of axis is axes.

______________________________________________________________________

____________________________________________________________________________

Just as maps plot geographic relationships, most graphs use Cartesian coordinates to show how variables are related. Cartesian coordinate systems entail two perpendicular lines, or axes, labeled x and y, that usually intersect at their respective zeros—the origin. The black lines in this figure are axes for standard Cartesian coordinates, and divide a “space” into four areas called quadrants, which are numbered I through IV, beginning from the northeast area and then moving in a counterclockwise direction.

Each point in this space is identified by an ordered pair of numbers denoted (x, y). The first coordinate, x, directs rightward movement if the x number is positive, or leftward movement if x is negative. The second coordinate, y, governs upward movement if y is positive, or downward movement if y is negative. Thus, quadrant I contains pairs for which both x and y are positive, quadrant II shows pairs for which x is negative and y is positive, quadrant III shows situations where both x and y are negative, and quadrant IV depicts positive values of x paired with negative values of y. Coordinates for the following points are depicted in Figure 5: (1, 1), (1, 4), (3, 3), (4, 1), (2, 5), (-2, 5), (-3, 3), (-1, 0), (-3, -3), (0, -4), and (3, -3). Be sure you can locate these coordinates before proceeding.

Remember, each pair gives two pieces of information: left-right for the value of x; then up-down for the value of y. Even though economists consider multidimensional problems, this technique allows us to deal with very complex issues by considering only two dimensions of a problem at a time. Most economic analyses use only the first, or positive, quadrant (quadrant I). Negative values for many economic variables would be meaningless; e.g., negative unemployment rates or negative consumption of a good are nonsensical concepts.