Find the slope of each line.y = 3x 2

Problem 1E Find the slope of each line. Through (4, 5) and (?1, 2)

Problem 3E Find the slope of each line. Through (8, 4) and (8, ?7)

Problem 4E Find the slope of each line. Through (1, 5) and (?2, 5)

Problem 2E Find the slope of each line. Through (5, ?4) and (1, 3)

Problem 5E Find the slope of each line. y = x

Problem 75A Tuition The table lists the annual cost (in dollars) of tuition and fees at private four-year colleges for selected years. (See Example) Source: The College Board. Year Tuition and Fees 2000 16,072 2002 18,060 2004 20,045 2006 22,308 2008 25,177 2009 26,273 a. Sketch a graph of the data. Do the data appear to lie roughly along a straight line? b. Let t = 0 correspond to the year 2000. Use the points (0, 16,072) and (9, 26,273) to determine a linear equation that models the data. What does the slope of the graph of the equation indicate? c. Discuss the accuracy of using this equation to estimate the cost of private college in 2025.

Problem 6E Find the slope of each line. y = 3x ? 2

Problem 7E Find the slope of each line. 5x ? 9y = 11

Problem 8E Find the slope of each line. 4x + 7y = 1

Problem 10E Find the slope of each line. The x-axis

Problem 9E Find the slope of each line. x = 5

Problem 11E Find the slope of each line. y = 8

Problem 15E In Exercise find an equation in slope-intercept form for each line. Through (1, 3), m = ?2

Problem 16E In Exercise find an equation in slope-intercept form for each line. Through (2, 4), m = ?1

Problem 17E In Exercise find an equation in slope-intercept form for each line. Through (?5, ?7), m = 0

Problem 12E Find the slope of each line. y = ?6

Problem 14E Find the slope of each line. A line perpendicular to 8x = 2y ?5

Problem 13E Find the slope of each line. A line parallel to 6x ? 3y = 12

Problem 18E In Exercise find an equation in slope-intercept form for each line. Through (?8, 1), with undefined slope

Problem 19E In Exercise find an equation in slope-intercept form for each line. Through (4, 2) and (1, 3)

Problem 22E In Exercise find an equation in slope-intercept form for each line. Through (?2, 3/4) and (2/3, 5/2)

Problem 20E In Exercise find an equation in slope-intercept form for each line. Through (8, ?1) and (4, 3)

Problem 25E In Exercise, find an equation for line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0. x-intercept ?6, y-intercept ?3

Problem 23E In Exercise find an equation in slope-intercept form for each line. Through (?8, 4) and (?8, 6)

Problem 26E In Exercise, find an equation for line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0. x-intercept ?2, y-intercept 4

Problem 24E In Exercise find an equation in slope-intercept form for each line. Through (?1, 3) and (0, 3)

Problem 21E In Exercise find an equation in slope-intercept form for each line. Through (2/3, 1/2) and (1/4, ?2)

Problem 28E In Exercise, find an equation for line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0. Horizontal, through (8, 7)

Problem 30E In Exercise, find an equation for line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0. Through (2, ?5), parallel to 2x ? y = ?4

Problem 29E In Exercise, find an equation for line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0. Through (?4, 6), parallel to 3x + 2y = 13

Problem 33E In Exercise, find an equation for line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0. The line with y-intercept 4 and perpendicular to x + 5y = 7

Problem 32E In Exercise, find an equation for line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0. Through (?2, 6), perpendicular to 2x ? 3y = 5

Problem 34E In Exercise, find an equation for line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0. The line with x-intercept ?2/3 and perpendicular to 2x ? y = 4

Problem 31E In Exercise, find an equation for line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0. Through (3, ?4), perpendicular to x + y = 4

Problem 35E Do the points (4, 3), (2, 0), and (?18, ?12) lie on the same line? Explain why or why not. (Hint:Find the slopes between the points.)

Problem 36E Find k so that the line through (4, ?1) and (k, 2) is a. parallel to 2x + 3y = 6, ________________ b. perpendicular to 5x ? 2y = ?1.

Problem 37E Use slopes to show that the quadrilateral with vertices at (1, 3), (?5/2, 2), (?7/2, 4), and (2, 1) is a parallelogram.

Problem 38E Use slopes to show that the square with vertices at (?2, 5), (4, 5), (4, ?1), and (?2, ?1) has diagonals that are perpendicular.

Problem 27E In Exercise, find an equation for line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0. Vertical, through (?6, 5)

Problem 40E For the lines in Exercise which of the following is closest to the slope of the line? (a) 1 (b) 2 (c) 3 (d) 21 (e) 22 (f) ?3

Problem 45E Graph equation. y = x ? 1

Problem 41E In Exercise estimate the slope of the lines.

Problem 42E In Exercises estimate the slope of the lines.

Problem 43E To show that two perpendicular lines, neither of which is vertical, have slopes with a product of –1, go through the following steps. Let line L1 have equation y = m1x + b1, and let L2 have equation y = m2x + b2, with m1 >0 and m2 < 0. Assume that L1 and L2 are perpendicular, and use right triangle MPN shown in the figure. Prove each of the following statements. a.MQ has length m1. b.QN has length ?m2. c. Triangles MPQ and PNQ are similar. d.m1 /1 = 1/(?m2) and m1m2 = ?1

Problem 39E For the lines in Exercise which of the following is closest to the slope of the line? (a) 1 (b) 2 (c) 3 (d) 21 (e) 22 (f) ?3

Problem 44E Consider the equation . a. Show that this equation represents a line by writing it in the form y = mx + b. ________________ b. Find the x- and y-intercepts of this line. ________________ c. Explain in your own words why the equation in this exercise is known as the intercept form of a line.

Problem 46E Graph equation. y = 4x + 5

Problem 50E Graph equation. 3x ? y = ?9

Problem 47E Graph equation. y = ?4x + 9

Problem 48E Graph equation. y = ?6x + 12

Problem 51E Graph equation. 3y ? 7x = ?21

Problem 52E Graph equation. 5y + 6x = 11

Problem 49E Graph equation. 2x ? 3y = 12

Problem 53E Graph equation. y = ?2

Problem 54E Graph equation. x = 4

Problem 55E Graph equation. x + 5 = 0

Problem 57E Graph equation. y = 2x

Problem 56E Graph equation. y + 8 = 0

Problem 59E Graph equation. x + 4y = 0

Problem 58E Graph equation. y = ?5x

Problem 60E Graph equation. 3x ? 5y = 0

Problem 61A Sales The sales of a small company were $27,000 in its second year of operation and $63,000 in its fifth year. Let y represent sales in the x th year of operation. Assume that the data can be approximated by a straight line. a. Find the slope of the sales line, and give an equation for the line in the form y = mx + b. ________________ b. Use your answer from part a to find out how many years must pass before the sales surpass $100,000.

Problem 62A Use of Cellular Telephones The following table shows the subscribership of cellular telephones in the United States (in millions) for even-numbered years between 2000 and 2008. Source: Time Almanac 2010. Year 2000 2002 2004 2006 2008 Subscribers (in millions) 109.48 140.77 182.14 233.04 270.33 a. Plot the data by letting t = 0 correspond to 2000. Discuss how well the data fit a straight line. b. Determine a linear equation that approximates the number of subscribers using the points (0, 109.48) and (8, 270.33). c. Repeat part b using the points (2, 140.77) and (8, 270.33). d. Discuss why your answers to parts b and c are similar but not identical. e. Using your equations from parts b and c, approximate the number of cellular phone subscribers in the year 2007. Compare your result with the actual value of 255.40 million.

Problem 64A HIV Infection The time interval between a person’s initial infection with HIV and that person’s eventual development of AIDS symptoms is an important issue. The method of infection with HIV affects the time interval before AIDS develops. One study of HIV patients who were infected by intravenous drug use found that 17% of the patients had AIDS after 4 years, and 33% had developed the disease after 7 years. The relationship between the time interval and the percentage of patients with AIDS can be modeled accurately with a linear equation. Source: Epidemiologic Review. a. Write a linear equation y = mt + b that models this data, using the ordered pairs (4, 0.17) and (7, 0.33). ________________ b. Use your equation from part a to predict the number of years before half of these patients will have AIDS.

Problem 65A Exercise Heart Rate To achieve the maximum benefit for the heart when exercising, your heart rate (in beats per minute) should be in the target heart rate zone. The lower limit of this zone is found by taking 70% of the difference between 220 and your age. The upper limit is found by using 85%. Source: Physical Fitness. a. Find formulas for the upper and lower limits (u and l) as linear equations involving the age x. ________________ b. What is the target heart rate zone for a 20-year-old? ________________ c. What is the target heart rate zone for a 40-year-old? ________________ d. Two women in an aerobics class stop to take their pulse and are surprised to find that they have the same pulse. One woman is 36 years older than the other and is working at the upper limit of her target heart rate zone. The younger woman is working at the lower limit of her target heart rate zone. What are the ages of the two women, and what is their pulse? ________________ e. Run for 10 minutes, take your pulse, and see if it is in your target heart rate zone. (After all, this is listed as an exercise!)

Problem 63A Consumer Price Index The Consumer Price Index (CPI) is a measure of the change in the cost of goods over time. The index was 100 for the three-year period centered on 1983. For simplicity, we will assume that the CPI was exactly 100 in 1983. Then the CPI of 215.3 in 2008 indicates that an item that cost $1.00 in 1983 would cost $2.15 in 2008. The CPI has been increasing approximately linearly over the last few decades. Source: Time Almanac 2010. a. Use this information to determine an equation for the CPI in terms of t, which represents the years since 1980. ________________ b. Based on the answer to part a, what was the predicted value of the CPI in 2000? Compare this estimate with the actual CPI of 172.2. ________________ c. Describe the rate at which the annual CPI is changing.

Problem 66A Ponies Trotting A 1991 study found that the peak vertical force on a trotting Shetland pony increased linearly with the pony’s speed, and that when the force reached a critical level, the pony switched from a trot to a gallop. For one pony, the critical force was 1.16 times its body weight. It experienced a force of 0.75 times its body weight at a speed of 2 meters per second and a force of 0.93 times its body weight at 3 meters per second. At what speed did the pony switch from a trot to a gallop? Source: Science.

Problem 67A Life Expectancy Some scientists believe there is a limit to how long humans can live. One supporting argument is that during the last century, life expectancy from age 65 has increased more slowly than life expectancy from birth, so eventually these two will be equal, at which point, according to these scientists, life expectancy should increase no further. In 1900, life expectancy at birth was 46 yr, and life expectancy at age 65 was 76 yr. In 2004, these figures had risen to 77.8 and 83.7, respectively. In both cases, the increase in life expectancy has been linear. Using these assumptions and the data given, find the maximum life expectancy for humans. Source: Science.

Problem 69A Health Insurance The percentage of adults in the United States without health insurance increased at a roughly linear rate from 1999, when it was 17.2%, to 2008, when it was 20.3%. Source: The New York Times. a. Determine a linear equation that approximates the percentage of adults in the United States without health insurance in terms of time t, where t represents the number of years since 1990. ________________ b. If this trend were to continue, in what year would the percentage of adults without health insurance be at least 25%?

Problem 70A Marriage The following table lists the U.S. median age at first marriage for men and women. The age at which both groups marry for the first time seems to be increasing at a roughly linear rate in recent decades. Let t correspond to the number of years since 1980. Source: U.S. Census Bureau. Age at First Marriage Year 1980 1985 1990 1995 2000 2005 Men 24.7 25.5 26.1 26.9 26.8 27.1 Women 22.0 23.3 23.9 24.5 25.1 25.3 a. Find a linear equation that approximates the data for men, using the data for the years 1980 and 2005. ________________ b. Repeat part a using the data for women. ________________ c. Which group seems to have the faster increase in median age at first marriage? ________________ d. In what year will the men’s median age at first marriage reach 30? ________________ e. When the men’s median age at first marriage is 30, what will the median age be for women?

Problem 68A Child Mortality Rate The mortality rate for children under 5 years of age around the world has been declining in a roughly linear fashion in recent years. The rate per 1000 live births was 90 in 1990 and 65 in 2008. Source: World Health Organization. a. Determine a linear equation that approximates the mortality rate in terms of time t , where trepresents the number of years since 1900. ________________ b. If this trend continues, in what year will the mortality rate first drop to 50 or below per 1000 live births?

Problem 71A Immigration In 1950, there were 249,187 immigrants admitted to the United States. In 2008, the number was 1,107,126. Source: 2008 Yearbook of Immigration Statistics. a. Assuming that the change in immigration is linear, write an equation expressing the number of immigrants, y, in terms of t, the number of years after 1900. ________________ b. Use your result in part a to predict the number of immigrants admitted to the United States in 2015. ________________ c. Considering the value of the y-intercept in your answer to part a, discuss the validity of using this equation to model the number of immigrants throughout the entire 20th century.

Problem 72A Global Warming In 1990, the Intergovernmental Panel on Climate Change predicted that the average temperature on Earth would rise 0.3°C per decade in the absence of international controls on greenhouse emissions. Let t measure the time in years since 1970, when the average global temperature was 15°C. Source: Science News. a. Find a linear equation giving the average global temperature in degrees Celsius in terms of t,the number of years since 1970. ________________ b. Scientists have estimated that the sea level will rise by 65 cm if the average global temperature rises to 19°C. According to your answer to part a, when would this occur?

Problem 73A Galactic Distance The table lists the distances (in megaparsecs where 1 megaparsec ?3.1 × 1019 km) and velocities (in kilometers per second) of four galaxies moving rapidly away from Earth. Source: Astronomical Methods and Calculations, and Fundamental Astronomy. Galaxy Distance Velocity Virga 15 1600 Ursa Minor 200 15,000 Corona Borealis 290 24,000 Bootes 520 40,000 a. Plot the data points letting x represent distance and y represent velocity. Do the points lie in an approximately linear pattern? ________________ b. Write a linear equation y = mx to model this data, using the ordered pair 1520, 40,0002. ________________ c. The galaxy Hydra has a velocity of 60,000 km per sec. Use your equation to approximate how far away it is from Earth. ________________ d. The value of m in the equation is called the Hubble constant. The Hubble constant can be used to estimate the age of the universe A (in years) using the formula Approximate A using your value of m.

Problem 74A News/Talk Radio From 2001 to 2007, the number of stations carrying news/talk radio increased at a roughly linear rate, from 1139 in 2001 to 1370 in 2007. Source: State of the Media. a. Find a linear equation expressing the number of stations carrying news/talk radio, y, in terms of t, the years since 2000. ________________ b. Use your answer from part a to predict the number of stations carrying news/talk radio in 2008. Compare with the actual number of 2046. Discuss how the linear trend from 2001 to 2007 might have changed in 2008.