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hendricks_beginning_algebra_1e_ch1_3

234 Chapter 3 Linear Equations in Two Variables 3b. In the equation y=- 2 3 x + 2, the slope m=- 2 3 and the y-intercept is (0, 2). Step 1: Plot the y-intercept (0, 2). Step 2: Since m=- 2 3 = -2 3 , we move down 2 units as we move right 3 units to get to another point. 6 4 2 –2 2 4 6 x –2 y (0, 2) (3, 0) 6 4 2 –2 4 6 x –2 y (0, 2) Down 2 Right 3 Step 3: Connect the points to obtain the graph of y=- 2 3 x + 2. (3, 0) 6 4 2 –2 2 4 6 x –2 y (0, 2) Student Check 3 Graph the line using its slope and y-intercept. a. y = 1 4 x + 3 b. y=-3x + 6 Troubleshooting Common Errors Some common errors associated with the concept of slope are shown next. �� ������������������������ ������������������ A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 4a. Find the slope between (3, -2) and (1, 7). �������������������������������������� ���������������������������������������������������������������� The values were substituted incorrectly. The numerator is the change in y and the denominator is the change in x. So, the slope between these points is m = y2 - y1 x2 - x1 m = 7 - (-2) 1 - (3) m = 9 -2 =- 9 2 Objective 4 ▶ Troubleshoot common errors. The slope is 3 - 1 -2 - 7 m = -9 m=- 2 9 m = 2


hendricks_beginning_algebra_1e_ch1_3
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