206 Chapter 3 Graphing Linear Equations in Two Variables 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. Graph the equation Solution: We will find three ordered pairs that are solutions to the equation In the table, we have selected arbitrary values for x and y and must complete the ordered pairs. Notice that in this case, we are choosing zero for x and zero for y to illustrate that the resulting equation is often easy to solve. 4x 3y 15 4132 3y 15 12 3y 15 Graphing a Linear Equation 4x 3y 15 4102 3y 15 3y 15 4x 3y 15 4x 3102 15 The completed table is shown with the corresponding ordered pairs. 10, 52 1334 , 02 13, 12 x y 0 5 0 334 3 1 To graph the equation, plot the three solutions and draw the line through the points (Figure 3-7). Skill Practice 5. Graph the equation . Graphing a Linear Equation 5 4 3 2 321 1 1 2 3 3y 3 Graph the equation y Solution: Because the y-variable is isolated in the equation, it is easy to substitute a value for x and simplify the right-hand side to find y. Since any number for x can be 1 3 x 1. Example 4 2x 3y 12 Figure 3-7 54 4 5 1 2 3 5 x (0, 5) (3, 1) ( 3 3, 0) 4 y 4 Answer 5. 6 5 4 3 2 1 y 43 2 1 2 3 4 5 6 1 1 2 3 4 x y 1 y 5 x 15 4 or 3 3 4 4x 15 10, 2 1 , 02 13, 2 x y 0 0 3 4x 3y 15. 4x 3y 15. Example 3 From the first row, From the second row, From the third row, substitute x 0: substitute y 0: substitute x 3:
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