Section 3.5 Writing Equations of Lines 259 approximately 20.2 million students enrolled in post-secondary degree granting institutions. (Source: National Center for Education Statistics) i. Assuming that enrollment is growing linearly, write an equation that represents the number of students (in millions) enrolled in post-secondary degree granting institutions x years after 2000. ii. Use the equation to estimate the enrollment in 2012. iii. When will the enrollment reach 28.26 million? Troubleshooting Common Errors Some common errors for writing equations of lines are shown next. �� ������������������������ �������������������� A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 6a. Write the equation of the line through (3, 0) with slope m = 2 3 . �������������������������������������� ���������������������������������������������������������������� The point (3, 0) is the x-intercept, not the y-intercept. So, we use the slope-intercept form to find the value of b. y = mx + b 0 = 2 3 (3) + b 0 = 2 + b - 2 = b p lue of . So, t uation 3 So, the equation is y = 2 3 x - 2. 6b. Write the equation of the line through (2, -1) and (5, -2). �������������������������������������� ���������������������������������������������������������������� The error was made in calculating the slope of the line. The slope should be m = change in y change in x = -2 - (-1) 5 - 2 =- 1 3 We can use the point-slope form to find the equation. y - y1 = m(x - x1) y - (-2)=- 1 3 (x - 5) y + 2=- 1 3 x + 5 3 y + 2 - 2=- 1 3 x + 5 3 - 2 y=- 1 3 x + 5 3 - 6 3 y=- 1 3 x - 1 3 Objective 6 ▶ Troubleshoot common errors. Since the point ( 3, 0) is given, the value of b = 3.the equation is y = 2 3 x + 3 The slope is m = 5 - 2 5 -2 - (-1) = 3 -1 =-3. o, the equatio = So, equation is y - y1 = m(x - x) 1 y - (-2) = -3 3(x - 5) y + 2 = -3x 3x + 15 y = -3x x + 13
hendricks_beginning_algebra_1e_ch1_3
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