229 b2.4 Linear Functions Find the slope of the line satisfying the given conditions. See Example 5. 41. through (2, -1) and (-3, -3) 42. through (-3, 4) and (2,-8) 43. through (5, 8) and (3, 12) 40 (e 45. through (5, 9) and (-2, 9) 44. through (5, -3) and (1,-7) 46. through (-2, 4) and (6, 4) 47. horizontal, through (5, 1) 48. horizontal, through (3, 5) 49. vertical, through (4, -7) 50. vertical, through (-8, 5) For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 51. у %3D Зх +5 53. 2y -3x 52. y 2x- 4 0.51 11 54.-4y 5x 56. 4х + 3у 3 12 55. 5x 2y 10 Graph the line passing through the given point and having the indicated slope. Plot two points on the line. See Example 7. 58. through (-2, 8), m = 3 57. through (-1, 3), m 2 60 through (-2. -3), m 1 1 2 II C-2

229 b2.4 Linear Functions Find the slope of the line satisfying the given conditions. See Example 5. 41. through (2, -1) and (-3, -3) 42. through (-3, 4) and (2,-8) 43. through (5, 8) and (3, 12) 40 (e 45. through (5, 9) and (-2, 9) 44. through (5, -3) and (1,-7) 46. through (-2, 4) and (6, 4) 47. horizontal, through (5, 1) 48. horizontal, through (3, 5) 49. vertical, through (4, -7) 50. vertical, through (-8, 5) For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 51. у %3D Зх +5 53. 2y -3x 52. y 2x- 4 0.51 11 54.-4y 5x 56. 4х + 3у 3 12 55. 5x 2y 10 Graph the line passing through the given point and having the indicated slope. Plot two points on the line. See Example 7. 58. through (-2, 8), m = 3 57. through (-1, 3), m 2 60 through (-2. -3), m 1 1 2 II C-2

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section4.1: Writing Equations In Slope-intercept Form

Problem 34E

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Suppose that average annual income (in dollars) forthe years 1990 through 1999 is given by the linearfunction: I(x)=1,054x+23,286 , where x is thenumber of years after 1990. Which of the followinginterprets the slope in the context of the problem? a. As of 1990, average annual income was $23,286. b. In the ten-year period from 1990-1999, averageannual income increased by a total of $1,054. c. Each year in the decade of the 1990s, averageannual income increased by $1,054. d. Average annual income rose to a level of $23,286 bythe end of 1999.
High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.
Later High School Graduates This is a continuation of Exercise 16. The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 2001 2.85 2003 2.98 2005 3.11 2007 3.24 a. Find the slope of the linear function modeling high school graduations, and explain in practical terms the meaning of the slope. b. Find a formula for a linear function that models these data. c. Express, using functional notation, the number graduating from high school in 2008, and then calculate the value. d. The actual number graduating from high school in 1994 was about 2.52 million. Compare this with the value given by the formula in part b and with your answer to part of Exercise 16. Which is closer to the actual value? In general terms, what was the trend in high school graduations from 1985 to 2007? 16. High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year.16 Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.
When Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the data are linear. But if data are not evenly spaced, then we must calculate the average rate of change over each interval to see whether the data are linear. If the average rate of change is constant, it is the slope of the linear function. This fact is used in Exercises 23 and 24. In the following table, show that the average rate of change from 2 to 5 is not the same as the average rate of change from 5 to 6. This shows that the data are not linear, even though the differences in y are constant. x 1 2 5 6 y 3 6 9 12
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Price of Amazons Kindle The following table shows the price of Amazons Kindle 2 e-book reader. It is adapted from data available on the web. Here time is measured in months since February 2009, when the Kindle was launched. Time Price 0 349 5 299 10 249 15 199 a. By calculating differences, show that these data can be modeled using a linear function. b. Find a linear formula that models these data. Be careful about the sign of the slope. c. What price does your formula from part b project for January 2012 35 months after the Kindle was launched? Note: The web data were the basis for speculation that some day the Kindle would be free.
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Manufacturing Cost The manager of a furniture factory finds that it costs 2200 to produce 100 chairs in one day and 4800 to produce 300 chairs in one day. a Assuming that the relationship between cost and the number of chairs produced is linear, find a linear function C that models the cost of producing x chairs in one day. b Draw a graph of C. What is the slope of this line? c At what rate does the factorys cost increase for every additional chair produced?
Pharmacology The numbers of prescriptions P (in thousands) filled at two pharmacies from 2012 through 2016 are shown in the table. (a) Use a graphing utility to create a scatter plot of the data for pharmacy A and find a linear model. Let t represent the year, with t=12 corresponding to 2012. Repeat the procedure for pharmacy B. (b) Assume that the models in part (a) can be used to represent future years. Will the number of prescriptions filled at pharmacy A ever exceed the number of prescriptions filled at pharmacy B? If so, when?
Employee Turnover The percentage of employees who cease their employment during a year is referred to as employee turnover, and it is a serious issue for businesses. The following table shows the cost, in millions of dollars, to Walmart for a given employee turnover percentage in a year.13 E = employee turnover 10 20 30 40 C = cost 250 400 550 700 a. Show that the data can be modeled by a linear function. b. Find the slope of the linear function. c. Find a linear model for the data. d. Use the result from part c to find the cost to Walmart if employee turnover is 33 in a year.
Market Demand This is a continuation of Exercise 13. The following table shows the quantity D of wheat, in billions of bushels, that wheat consumers are willing to purchase in a year at a prince P, in dollars per bushel. D = quantity of wheat P = price 1.0 2.05 1.5 1.75 2.0 1.45 2.5 1.15 In economics, it is customary to plot D on the horizontal axis and P on the vertical axis, so we will think of D as a variable and of P as a function of D. a. Show that these data can be modeled by a linear function, and find its formula. b. Add the graph of the linear formula you found in part a, which is called the market demand curve, to your graph of the market supply curve from Exercise 13. c. Explain why the market demand curve should be decreasing. d. The equilibrium price is the price determined by the intersection of the market demand curve and the market supply curve. Find the equilibrium price determined by your graph in part b. 13. Market supply The following table shows the quantity S of wheat, in billions of bushels, that wheat supplies are willing to produce in a year and offer for sale at a price P, in dollars per bushel. S = quantity of wheat P = price 1.0 1.35 1.5 2.40 2.0 3.45 2.5 4.50 In economics, it is customary to plot S on the horizontal axis and P on the vertical axis, so we will think of S as a variable and of P as a function of S. a. Show that these data can be modeled by a linear function, and find its formula. b. Make a graph of the linear formula you found in part a. This is called the market supply curve. c. Explain why the market supply curve should be increasing. Hint: Think about what should happen when the price increases. d. How much wheat would suppliers be willing to produce in a year and offer for sale at a price of 3.90 per bushel?