Summary 261 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, find the x- and y-intercepts. x-intercept y-intercept 2x 102 2 2102 y 2 2x 2 0 y 2 x 1 y 2 11, 02 10, 22 Example 3 x 3 represents a y 3 represents a 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. To find the x-intercept, let y 0 and solve for x. A y-intercept of a graph is a point (0, b) where the graph intersects the y-axis. To find the y-intercept, let and solve for y. 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. x 0 Ax By C 54 4 5 2 3 4 5 2 1 1 x y (0, 2) (1, 4) (1, 0) 5 y 1 543 1 2 3 4 5 2 1 1 2 3 4 5 x 4 3 2 x 3 5 y 1 543 1 2 3 4 5 21 1 2 3 4 5 x 4 3 2 y 3 x y 0 2 1 4 1 0
miller_beginning_intermediate_algebra_4e_ch1_3
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