223CHAPTER14 The Cartesian Plane
In the 1600s, the French mathematician Rene Descartes (pronounced “re-NAY day-CART”)
invented a way to illustrate relations and functions. It became a graphing scheme now known
asCartesian (pronounced “car-TEE-zhun”) coordinates or the Cartesian plane.Two Number Lines
The Cartesian plane is put together by placing two real-number lines so they intersect at a
right angle. The number lines usually intersect at their 0 points. The point where the axes
intersect is called the origin.Variables and ordered pairs
Figure 14-1 shows a simple set of Cartesian coordinates. The independent variable is por-
trayed along a horizontal line, and the dependent variable is portrayed along a vertical line.
The number-line scales are graduated in increments of the same size.
Figure 14-2 shows how several ordered pairs of the form (x,y) are plotted as points on the
Cartesian plane. Here, x is the independent variable and y is the dependent variable.The quadrants
Any pair of intersecting lines divides a plane into four parts. In the Cartesian system, these
parts are called quadrants (Fig. 14-3):- In the first quadrant, both variables are positive.
- In the second quadrant, the independent variable is negative and the dependent variable
is positive. - In the third quadrant, both variables are negative.
- In the fourth quadrant, the independent variable is positive and the dependent variable
is negative.
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