318 CHAPTER 2 Graphs and Functions (Modeling) Work each problem. 57. Distance from Home The graph depicts the distance y that a person driving a car on a straight road is from home after x hours. Interpret the graph. At what speeds did the car travel? 58. Job Market The figure shows the number of jobs gained or lost in a recent period from September to May. (a) Is this the graph of a function? (b) In what month were the most jobs lost? the most gained? (c) What was the largest number of jobs lost? of jobs gained? (d) Do these data show an upward or a downward trend? If so, which is it? 59. E-Filing Tax Returns The percent of tax returns filed electronically in 2001 was 30.7%. In 2018, the figure was 92.0%. (Data from Internal Revenue Service.) (a) Use the information given for the years 2001 and 2018, letting x = 0 represent 2001, x = 17 represent 2018, and y represent the percent of returns filed electronically, to find a linear equation that models the data. Write the equation in slope-intercept form with the slope rounded to the nearest hundredth. Interpret the slope of the graph of this equation. (b) Use the equation from part (a) to approximate the percent of tax returns that were filed electronically in 2009. Round to the nearest tenth. 60. Spread of News A piece of information is announced by mass media in a small town. The figure shows the number of people who have heard the news after t days. Find the average rate of change, to the nearest person, of the spread of the news between day 4 and day 9. For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form. 61. through 13, -52 with slope -2 62. through 1-2, 42 and 11, 32 63. through 12, -12, parallel to 3x - y = 1 64. x-intercept 1-3, 02, y-intercept 10, 52 S O N D J F M A M –5000 –10,000 0 5000 10,000 Jobs gained or lost Month Job Market Trends 0 1 2 3 4 5 6 10 20 30 40 50 60 70 x y Time (in hours) Distance from Home Distance (in miles) Time (in days) Spread of News y = f(t) 2 4 6 8 10 12 25,000 20,000 15,000 (9, 22,365) (4, 15,803) 10,000 People 5000 0 y t 65. through 12, -102, perpendicular to a line with undefined slope 66. through 10, 52, perpendicular to 8x + 5y = 3 67. through 1-7, 42, perpendicular to y = 8 68. through 13, -52, parallel to y = 4
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