TABLE OF CONTENTS We now expand our discussion of the single-variable linear equation to the general linear equation in two variables, x and y. Some examples of linear equations are
The graph of a linear equation is a line. Although drawing a line is a simple geometric construction, graphing a line requires knowledge of algebraic concepts.
The Cartesian plane is a two-dimensional space formed by intersecting, in a perpendicular fashion, two number lines at their zeros. The number line placed horizontally is called the x-axis and the number line placed vertically is called the y-axis of the Cartesian plane. Since the number lines are of infinite length the resulting plane is of infinite area. Consequently, we only draw the portion of the plane immediately surrounding the point of intersection of the number lines.
The idea of plotting mathematical relationships using x, y-coordinates called ordered pairs was formulated around 1630 by Pierre de Fermat and Ren Descartes, mathematicians who worked separately on the same concept.
Figure 10.1 shows the Cartesian plane, which is also called the ( x, y)- coordinate plane. Notice how drawing lines through each integer value on both the x- and y-axes forms a grid. Thus drawn, the intersections mark points in the plane. Each point defines a unique location in the plane with an x component (or abscissa) and a y component (or ordinate), called the x
