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Section 3.2 Linear Equations in Two Variables 223 Graphing a Linear Equation Graph the equation x 2y 8. Solution: We will find three ordered pairs that are solutions to x 2y 8. To find the ordered pairs choose arbitrary values of x or of y. Three choices are recorded in the table. To complete the table, individually substitute each choice into the equation and solve for the remaining variable. The substituted value and the solution to the equation form an ordered pair. Example 2 Skill Practice Graph the equation. 4. 2x y 6 10, 42. Answer 4. 5 4 3 2 1 y 543 2 1 1 2 3 4 5 1 2 3 4 5 x 12, 2 1 , 12 10, 2 x y 2 1 0 From the first row, substitute x 2: x 2y 8 122 2y 8 2y 8 2 2y 6 y 3 From the second row, substitute y 1: x 2y 8 x 2112 8 x 2 8 x 8 2 x 6 From the third row, substitute x 0: x 2y 8 102 2y 8 2y 8 y 4 The completed table is shown with the corresponding ordered pairs. 12, 32 16, 12 10, 42 x y 2 3 6 1 0 4 To graph the equation, plot the three solutions and draw the line through the points (Figure 3-6). 3 2 21 1 1 2 3 4 5 6 7 1 2 3 4 5 6 7 y x (0, 4) (2, 3) 8 (6, 1) Figure 3-6 In Example 2, the original values for x and y given in the table were chosen arbitrarily by the authors. It is important to note, however, that once you choose an arbitrary value for x, the corresponding y value is determined by the equation. Similarly, once you choose an arbitrary value for y, the x value is determined by the equation. Classroom Example: p. 231, Exercise 18 TIP: When choosing an arbitrary value for a variable, try to choose values that are convenient to graph. For example, we could let x 1000 and solve for y. However, then we would need a very large graph or a large scale on the axes. Avoiding Mistakes Only two points are needed to graph a line. However, in Example 2, we found a third ordered pair, Notice that this point “lines up” with the other two points. If the three points do not line up, then we know that a mistake was made in solving for at least one of the ordered pairs.


miller_introductory_algebra_3e_ch1_3
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