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messersmith_power_intermediate_algebra_1e_ch4_7_10

3 Graph a Linear Equation in Two Variables by Plotting Points We saw in Example 2 that the ordered pair (1, 3) is a solution of the equation 4x  5y 11. This is just one solution, however. The equation has an infi nite number of solutions of the form (x, y), and we can represent these solutions with a graph on the Cartesian coordinate system. The following table of values contains the solution we just verifi ed as well as other solutions of 4x 5y 11. Plot the points and connect them with a straight line. The line represents all solutions of the equation. 4x 5y 11 4(1) 5(3) 4 15 11 4(4) 5(1) 16 (5) 11 4(9) 5(5) 36 (25) 11 4(0) 5 a11 5 b 0 11 11 4 a11 4 b 5(0) 11 0 11 While equations like x 3 5 and 2(t 7) 3t 10 are linear equations in one variable, the equation 4x 5y 11 is an example of a linear equation in two variables. The graph of a linear equation in two variables is a line, and every point on the  line is a solution of the equation. Definition A linear equation in two variables can be written in the form Ax By C, where A, B, and C are real numbers and where both A and B do not equal zero. Other examples of linear equations in two variables are 3x 5y 10 y (We can write x 8 as x 0y 8, therefore it is a linear equation in two variables.) A solution to a linear equation in two variables is written as an ordered pair. x y 1 3 4 1 9 5 0 11 5 11 4 0 EXAMPLE 3 Graph x 2y 4. y 6 (1, 3) 5 4x 5y 11 1 1 , 0 4 (4, 1) (0,11) 5 10 6 (9, 5) 1 2 x 7 9s 2t 4 x 8 Solution We will fi nd three ordered pairs which satisfy the equation. Let’s complete a table of values for x 0, x 2, and x 4. x 0: x 2y 4 x 2: x 2y 4 x 4: x 2y 4 (0) 2y 4 (2) 2y 4 (4) 2y 4 2y 4 2 2y 4 4 2y 4 y 2 2y 6 2y 0 y 3 y 0 x www.mhhe.com/messersmith SECTION 4.1 Introduction to Linear Equations in Two Variables 143


messersmith_power_intermediate_algebra_1e_ch4_7_10
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