Summary 279 Section 3.2 Linear Equations in Two Variables Examples Example 1 Graph the equation 2x y 2 . Select arbitrary values of x or y such as those shown in the table. Then complete the table to find the corresponding ordered pairs. 5 4 3 321 1 2 3 Example 2 For the line 2x y 2, the x-intercept is (1, 0) and the y-intercept is (0, 2). x 3 represents a y 3 represents a 5 y 1 2 1 543 1 2 3 4 5 1 2 3 4 5 x 4 3 2 x 3 5 y 1 21 543 1 2 3 4 5 1 2 3 4 5 x 4 3 2 y 3 Ax By C A vertical line can be represented by an equation of the form x k. A horizontal line can be represented by an equation of the form y k. Example 3 vertical line horizontal line Key Concepts An equation written in the form (where A and B are not both zero) is a linear equation in two variables. A solution to a linear equation in x and y is an ordered pair (x, y) that makes the equation a true statement. The graph of the set of all solutions of a linear equation in two variables is a line in a rectangular coordinate system. A linear equation can be graphed by finding at least two solutions and graphing the line through the points. An x-intercept of a graph is a point (a, 0) where the graph intersects the x-axis. A y-intercept of a graph is a point (0, b) where the graph intersects the y-axis. x y 0 2 1 4 1 0 (0, 2) (1, 4) (1, 0) 54 4 5 2 3 4 5 2 1 1 x y
miller_introductory_algebra_3e_ch1_3
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