Lesson Master 6-1B. USES Objective E. Questions on SPUR Objectives. In 1 5, use the chart showing the percent of households that had a computer.

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1 Back to Lesson B USES Objective E In 1 5, use the chart showing the percent of households that had a computer. Year Percent of Households Make a line graph for the number of households that had a computer from 1989 to In which 4-ear time period is the increase in the percent of households that had a computer the greatest? 3. What is the rate of change of the percent of households that had a computer from 1993 to 2001? 4. Which is steeper, the segment joining (1989, 15.0) to (1993, 22.8) or the segment joining (1993, 22.8) to (1997, 36.6)? In 5 8, use the chart showing the average cost per compact disc. Year Average Cost $13.07 $12.78 $12.75 $13.48 $ Make a line graph for the average cost per compact disc. Copright Wright Group/McGraw-Hill 6. Identif all two-ear time periods where the rate of change is negative. 7. What does a negative rate of change represent in this situation? Algebra 227

2 Back to Lesson B page 2 8. Which two-ear time period had the greatest rate of change in the average cost per compact disc? In 9 15, refer to the graph below of the total amount of rain that fell in Lake Zurich, Illinois, for the fi rst 20 das in September, Total Rainfall (inches) Da In which 1-da time period did it rain the most? 10. Is the rate of change from da 16 to da 19 positive, negative, or zero? 11. What is the rate of change from da 19 to da 20? 12. Eplain wh the rate of change in total rainfall between an two das would not be negative. 13. What was the average rainfall per da for the first 20 das in September? 14. Which is steeper, the segment joining (3, 0.1) and (4, 0.5) or the segment joining (9, 0.7) and (10, 1.1)? 15. Between which das was there no change in rainfall? Copright Wright Group/McGraw-Hill 228 Algebra

3 Back to Lesson B SKILLS Objective A In 1 and 2, fi nd the slope of the line through the two points. 1. (5, 20) and (3, 15) 2. ( 7, 5) and (7, 5) In 3 and 4, refer to the graph below. Find the slope of the line. p 5 4 q line p 4. line q 5. The points (3, 2) and ( 4, a) lie on a line with slope 4 7. Find the value of a. 6. A line has equation = Find its slope. 4 In 7 9, an equation for a line is given. Find two points on the line. Then fi nd the slope of the line. 7. = ; 8. = 5-2 ; = 9 ; 10. Calculate the slope of the line through (10, 7) and ( 10, 7). In 11 14, use the table that gives the number of toothpicks used in the sequence of designs below. Number of Triangles Number of Toothpicks ?? Copright Wright Group/McGraw-Hill 11. If the design is continued to complete the net row of the table, what ordered pair is given? 230 Algebra

4 Back to Lesson B page How do ou know that the points in the table lie on the same line? 13. Find the rate of change between an two points on the line. 14. Describe the real-world meaning of the rate of change. PROPERTIES Objective D 15. A line with a slope of zero passes through the points (v, k) and (w, z). How is k related to z? In 16 18, use the fi gure below. v t u r s 16. Which lines(s) could have the indicated slope? a. positive slope b. negative slope Copright Wright Group/McGraw-Hill c. slope = Which line has the steepest negative slope? 18. Which line could have the equation =? 19. Do the points (8, 9), ( 2, 39), and (6, 15) lie on the same line? How can ou tell? 20. The points (2, 3) and (, 8) are on a line with slope Find the value of. Algebra 231

5 Back to Lesson B PROPERTIES Objective D 1. A horizontal line passes through (a, 1) and (b, 5). How are a and b related? 2. A line has slope of 2. As ou move right three unit on the line, how 3 man units do ou move down? 3. A line with an undefined slope passes through (3, 2) and (, 2). What is the value of? 4. A line has an undefined slope. Some coordinates of the points on the line are given in the table. a. Fill in the remaining entries in the table b. Eplain wh the line has an undefined slope. 5. Multiple Choice. Which term best describes the slope of a line with no vertical change? Copright Wright Group/McGraw-Hill A positive B negative C zero D undefined USES Objective E 6. Kenned uses an etension ladder to clean out leaves from the gutters of his house. The ladder rests against the gutters 16 feet off the ground and the base of the ladder is 8 feet from the bottom of the house. At what slope is the ladder resting against the house? 7. A child climbs up a 4-foot rock wall to reach the top of a slide. The end of the slide is 8 feet from the bottom of the wall. What is the slope at which the child slides down the slide? Algebra 233

6 Back to Lesson B page 2 In 8 10, use this information: In Northfi eld, the building code specifi es that a handicap-access ramp can rise no more than 1 inch for each foot of ground level. 8. Draw such a ramp. 9. What is the slope of such a ramp? 10. The maimum height of a handicap-access ramp is 30 inches. How man feet along the ground will a ramp of this tpe take up? d 11. One of the steepest streets in San Francisco is 22nd Street. It rises 1 foot for ever 3.17 feet of level ground. What is the slope of this street? REPRESENTATIONS Objective H In 12 15, a line s slope and a point on it are given. Graph the line. 12. point (4, 7), slope point ( 5, 6), undefined slope 14. point (4, 7), slope point ( 5, 6), slope 2 5 REPRESENTATIONS Objective D 16. Give the slope of the line. 234 Algebra Copright Wright Group/McGraw-Hill

7 Back to Lesson B SKILLS Objective B In 1 and 2, write an equation of the line in slope-intercept form with the following characteristics. 1. slope = 3, -intercept slope = 1, -intercept 7 In 3 5, refer to the graph at the right. 3. Determine the slope of the line. 4. Determine the -intercept of the line (3, 2) (0, 4) 5. Write an equation of the line in slope-intercept form. In 6 8, refer to the graph at the right. 6. Determine the slope of the line. 7. Determine the -intercept of the line (1, 5) 4 2 (0, 0) Write an equation of the line in slope-intercept form. Copright Wright Group/McGraw-Hill USES Objective F 9. The Dowz famil bought a package of paper towels that contained 12 rolls. Ever 5 das, the need to open a new roll from the package. If this situation were graphed with as the total number of paper-towel rolls left after d das, determine the following. a. the -intercept b. the slope c. an equation of the line Algebra 237

8 Back to Lesson B page Crosb spent $25 for some part favors. He still wants to bu some part hats that cost $3 each. If this situation were graphed with as the total cost of the part items when Crosb bus hats, determine the following. a. -intercept b. slope c. an equation of the line d. If Crosb purchased 25 hats, what was the total cost (before ta) of the part items? REPRESENTATIONS Objective H In 11 and 12, an equation of a line in slope-intercept form is given. Graph the line. 11. = = Graph the equation in Question 9c. 14. Graph the equation in Question 10c. d Copright Wright Group/McGraw-Hill 238 Algebra

9 Back to Lesson B SKILLS Objective B In 1 6, write an equation of the line given the slope and one point on the line. 1. slope 1, point (8, 3) 2. slope 2, point ( 1, 4) 4 3. slope 2 2, point ( 6, 5) 4. slope 5, point ( 3 5, 12) 5. slope 0, point ( 6, 15) 6. slope 1, point (2.4, 3.2) 2 7. The slope of a line is 5 and the -intercept is 2. Write an equation of the line. 8. The slope of a line is 1 and the -intercept is 4. Write an 3 equation of the line. 9. What is the equation of a horizontal line through the point ( 2, 3 _ 4 )? 10. Determine an equation for the line that contains (0, 2) and is parallel to the line with equation = 3 5. In 11 and 12, the slopes of two lines are reciprocals. 11. An equation of one line is = What is the slope of the 8 second line? 12. Find the equation of the second line if it passes through the point (14, 10). Copright Wright Group/McGraw-Hill 240 Algebra

10 Back to Lesson B page 2 USES Objective F 13. A suburban school district had an enrollment of 7,200 students in the ear Enrollment has been growing at a fairl constant rate of 50 students per ear. a. Write an ordered pair described b the information. b. Write the slope described b the information. c. Write an equation relating the number of students in the school district and the number of ears since d. Estimate the total enrollment the school district might epect for the ear 2010, if this rate of growth remains stead. 14. Si hundred fift people attended a dance recital. When it was over, the theater emptied at a rate of 125 people ever 5 minutes. a. Write an ordered pair described b the information. b. Write the slope described b the information. c. Write an equation to represent the number of people p in the theater after m minutes. d. How long will it take to empt the theater? In 15 and 16, use the table below. It represents the admission and parking costs at a zoo when Cherise went with her famil and some friends. Everone rode in one car and onl 2 adults went to the zoo. Parking $6.75 Adult admission $7.00 Copright Wright Group/McGraw-Hill Child admission $ Let c represent the number of children who went to the zoo and let t represent the total cost of admission to the zoo. Write an equation relating t and c. 16. If the total costs for parking and admission were $38.25, how man children went to the zoo on this trip? Algebra 241

11 Back to Lesson B SKILLS Objective B In 1 6, write an equation in slope-intercept form of the line through the two given points. 1. (2, 4) and (5, 13) 2. (6, 3) and (22, 11) 3. ( 1.5, 0.5) and ( 3, 0) 4. (5, 13) and (10, 10) 5. (8, 3) and ( 12, 2) 6. ( 3 4, 2 3 ) and ( 1 2, 1 ) 7. Write an equation of the line through ( 2, 3) and (4, 1). 8. Check our answer to Question 7 b graphing the line. 9. Write an equation for the line with -intercept 4 and -intercept 5. Copright Wright Group/McGraw-Hill 10. Write an equation for the line that produced 11. Write an equation of the line shown below. the table of values shown below Algebra 243

12 Back to Lesson B page 2 USES Objective F 12. Black Frida, the da after Thanksgiving, is characterized b millions of shoppers and billions of dollars in retail sales. Retail sales in 2005 were about $8.45 billion and in 2006 were about $8.96 billion. a. Epress the data as two ordered pairs. b. Find the slope of the line through these points. c. Eplain what the slope represents in this situation. d. What was the percent of increase in sales? e. Write an equation for in terms of for the relationship. 13. The total sales of golf equipment in the United States in 2004 were $3,198.2 million. In 2005 the total sales were $3,474.4 million. Assume there is a linear relationship between the number of ears since 2004 and the sales in millions s of golf equipment. a. Epress the data as two ordered pairs. b. Find the slope of the line through these points. c. Eplain what the slope represents in this situation. d. Write an equation for in terms of s for this relationship. e. Use our equation from Part d to predict the total sales of golf equipment in Copright Wright Group/McGraw-Hill 244 Algebra

13 Back to Lesson B USES Objective G In 1 7, use the table at the right of the average dail number of passengers in Januar at Baltimore/Washington International Thurgood Marshall Airport. 1. Draw a scatterplot of these ordered pairs with representing the number of ears since 2002 and representing the average dail number of airline passengers for Januar. Average Dail Number of Passengers for Januar 53,000 51,000 49,000 47,000 45,000 43,000 41, Years since 2002 Year Average Number of Passengers per Da , , , , , Use our calculator to find an equation for the regression line for these ordered pairs. 3. Graph the regression line on our scatterplot. B how much does the 2005 average deviate from the linear regression equation s predicted average for that ear? 4. According to our equation, b about how man passengers does the dail average for Januar increase b each ear? 5. Use our equation to predict the average dail number of passengers in Januar, Use our equation to find what ear the average dail number of airline passengers in Januar will be about 51, Is the average dail number of passengers for Januar, 2006, greater or less than what the equation predicted? Wh do ou think this happened? Copright Wright Group/McGraw-Hill 246 Algebra

14 Back to Lesson B page 2 In 8 13 use the table below of the slugging percentage (SLG) for Aramis Ramirez for each season from 1998 to In baseball statistics, the slugging percentage is a measure of the power of a hitter. SLG = number of bases gained with hits number of times at bat 8. Draw a scatterplot of these ordered pairs with representing the number of ears since 1998 and representing the slugging percentage. SLG (thousandths) Years since Use our calculator to find an equation for the regression line for this data. Season SLG Graph the regression line on our scatterplot. In which ear does the SLG deviate the most from the equation? 11. According to our equation, b about how much does Ramirez s SLG increase each ear? 12. Use our equation to predict Ramirez s SLG in Was Ramirez s SLG for 2006 greater or less than our equation predicted? Wh do ou think this happened? Copright Wright Group/McGraw-Hill Algebra 247

15 Back to Lesson B SKILLS Objective C In 1 6, rewrite the equation in standard form with integer coeffi cients. 1. = = = = = = In 7 and 8, an equation in slope intercept form is given. Find an equivalent equation in standard form with integer coeffi cients. 7. = 7 8. = USES Objective F On December 3, 2006, the Jacksonville Jaguars defeated the Miami Dolphins b a score of 24 to 10. Each team scored onl 7 points (touchdown and etra point) or 3 points (fi eld goal). 9. For the Jaguars, a. write an equation in standard form that describes the relationship between touchdowns/etra points t and field goals f. Copright Wright Group/McGraw-Hill b. give two solutions to this equation, where t and f are integers. 10. For the Dolphins, a. write an equation in standard form that describes the relationship between touchdowns/etra points t and field goals f. b. give a solution to this equation, where t and f are integers. Algebra 249

16 Back to Lesson B page A furniture store emploee earns $8 an hour and a 20% commission on his sales. His earnings for one week were $1,500. Let = the number of hours the emploee worked and = the amount of his sales. a. Write an equation in standard form that describes all the different possible combinations of the hours the emploee worked and the amount of his sales. b. Give three possible pairs of values of and. c. Graph all possible solutions. d. If the emploee worked 40 hours, what were his sales? e. Give the coordinates of the point on the graph corresponding to our answer to Part d. 12. Nanc went to the Ever Blooming Thing garden center and bought small geraniums g for $1.25 each and perennial plants p for $3.50 each. She spent $70, without ta. a. Write an equation in standard form that describes the relationship between g and p. b. Give three solutions to our equation from Part a. c. If the $70 included the cost of 15 perennial plants, how man geraniums did Nanc bu? Total Sales in Dollars 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1, Number of Hours REPRESENTATIONS Objective H In 13 and 14, an equation in slope-intercept form is given. Find the - and -intercepts of the graph of the line, and then graph the line = = 35 Copright Wright Group/McGraw-Hill 250 Algebra

17 Back to Lesson A REPRESENTATIONS Objective I In 1 6, graph all points (, ) that satisf the inequalit < 7 3. > < A bo of herbal tea contains 20 bags. Each cup requires 1 tea bag and each pitcher requires 4 tea bags. a. Write an inequalit that gives the maimum number of cups c and pitchers p that can be brewed from 1 bo of tea bags. b. Give two possible combinations of c and p. Copright Wright Group/McGraw-Hill Algebra 251