38. The table lists the annual profit (in billions of dollars) for Delta Airlines between 2000 and 2006. (Section 3.1, Objective 5 ) (Sources: The Atlanta Journal-Constitution, Sept. 15, 2005 and www.delta.com) Years After 2000 0 1 2 3 4 5 6 Annual profit (in billions) 1.23 -1.21 -1.27 -0.773 -5.2 -1.46 0.058 a. Write an ordered pair (x, y) that corresponds to each year between 2000 and 2006, where x is the number of years after 2000 and y is the profit of Delta Airlines (in billions of dollars). b. Interpret the meaning of the first and last ordered pairs from part (a) in the context of the problem. c. In what year was the profit the highest? The lowest? d. Make a scatter plot of the data. 39. Graph each equation. Identify at least two points on the graph. (Section 3.2, Objectives 2–4 ) a. 2x + 7y = 14 b. y + 5 = 0 c. x - 6 = 0 d. 3x + y = 0 e. x - 0.5y = 1 f. y = -2x + 1 g. 0.4x - 0.5y = 2 40. The number of full-time classroom teachers (in thousands) in elementary and secondary schools in the United States can be modeled by the equation y = 32.5x + 3649.1, where x is the number of years after 2008. (Section 3.2, Objective 5 ) (Source: http://www .census.gov/compendia/statab/2010/tables/10s0216.pdf ) a. Find the y-intercept and interpret its meaning. Is this realistic? b. How many full-time classroom teachers in elementary and secondary schools does the model predict in 2010? c. How many full-time classroom teachers in elementary and secondary schools does the model predict in 2014? d. Use the intercepts to graph the equation. 41. Find the slope of each line described. (Section 3.3, Objectives 1, 3, 4 ) a. y=- 2 3 x + 4 b. passes through (2, -4) and (4, 0) c. y = 6 d. x = -5 e. passes through (-3.2, -1.4) and (1.2, -10.2) f. 5x - 3y = 2 g. 2 y 2 4 –2 –4 –2 –4 –6 x 42. Graph each line described. Label two points on the line. (Section 3.4, Objective 2) a. m = 2, (0, 5) b. m = 5, (0, 3) c. m = -3, (0, 1) d. m = -4, b = 3 e. m = 0.5, b = -2 f. m = undefined, (-2, 1) g. m = 0, (3, -4) 43. The number of associate degrees (in thousands) conferred in all higher education institutions can be modeled by the equation y = 10.93x + 73,764, where x is the number of years after 2008. Interpret the meaning of the slope and y-intercept in the context of the problem. Use the slope and y-intercept to create a table of three ordered pairs that satisfy the given equation. (Section 3.4, Objective 1) 44. Determine if each pair of lines is parallel, perpendicular, or neither. (Section 3.4, Objective 3) a. y = 3 2 x + 1 and y = 3 2 x - 4 b. 2x + 5y = 1 and 2x - 5y = 2 c. y = 1 and x = 2 d. y = 0.5x and y = -2x 45. Graph the line that is parallel to y = -3x + 2 and passes through the point (-4, 1). (Section 3.4, Objective 4) 46. Graph the line that is perpendicular to y = 2x - 3 and passes through the point (-2, 3). (Section 3.4, Objective 4) 47. Write the equation of the line described. Express your answer in slope-intercept form and in standard form if possible. (Section 3.5, Objectives 1– 4) a. (-5, 6) and (2, -1) b. m = undefined, (3, 6) c. m = 0, (0, 12) d. (-2, 4), parallel to 2 x + y = 5 e. (3, -5), perpendicular to x + 3y = 1 f. x-intercept (-4, 0) and y-intercept (0, 3) g. m = -4, x-intercept: (2, 0) 48. Michael enrolls in a fitness club. There is a one-time membership fee of $250 plus a monthly charge of $40. (Section 3.5, Objective 5) a. Write a linear equation that represents the total cost of joining the fitness club, where x is the number of months Michael is a member. b. How much money has Michael spent for his fitness club membership if he has been a member for 1 year? c. How long has Michael been a member of the club if he pays the fitness club a total of $1450? 290 Chapter 3 Linear Equations in Two Variables
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