Section 3.1 The Coordinate System, Graphing Equations, and the Midpoint Formula 159 Objective 7 Examples A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. Solutions 7a. Plot the point (0, -3). Incorrect Solution Correct Solution and Explanation To plot (0, -3), we must not move left or right from the origin but move down 3 units. 2 2 4 4 –2 –4 –2 –4 (0 –3) x y 4 7b. Determine if a- 2 3 , -1b is a solution of y = -6x - 5. Incorrect Solution Correct Solution and Explanation y = −6x − 5 The error was made in multiplying the values -6 and - 2 3 . Their product is 4 not -4. y = −6x − 5 −1 = −6a- 2 3 b− 5 −1 = 4 −5 −1 = −1 Since the statement is true, the ordered pair is a solution of the equation. −1 −6 a- 2 3 b− 5 −1 = −4 − 5 −1 = −9 Since the statement is false, the ordered pair is not a solution of the equation. ANSWERS TO STUDENT CHECKS Student Check 1 a. Quadrant III b. Quadrant IV c. Quadrant II d. y-axis e. x-axis f. Quadrant I Student Check 2 a. (2, 6) and a1 3 , 1b are solutions. b. a1 2 , 0b , (0, -1), and a11 2 , 10b are solutions. c. (-3, 0) and (-4, 1) are solutions. d. (-1, 9) is a solution. Student Check 3 a. y = x + 3 b. y = x2 + 1 6 2 2 4 –2 –6 –4 –2 –4 x y 6 2 –4 –2 x 2 4 4 –2 y y 5 1 = he a ution equation 2 2 f c –2 –4 –2 –4 x y 2 4 –2 –4 –2 –4 x y 2
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