-3 Stud Guide and Intervention Rate of Change Rate of change is a ratio that compares how much one quantit changes, on average, relative to the change in another quantit. Eample Average Rate of Change = = = = Find the average rate of change for the data in the table. change in change in change in Elevation of the Sun change in Time 8 11:00 A.M. 7:00 A.M. 78 hours = 19.5 degrees per hour Elevation of the Sun (in degrees) 5 Time 7:00 A.M. 8:00 A.M. 9:00 A.M. 10:00 A.M. 8 11:00 A.M. Eercises Find the rate of change for each set of data. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 1. Time P.M. People in auditorium 7:15 7: 1 7: 71 7:30 101 7:0 151 3. Time (minutes) 11 19 8 5. Time (seconds) 13 15 3 7 Vehicles through tunnel 1,10,131,7,970 3,3 Water through Channel (liters),17,70 5,30 8,3 37,01. Time (minutes) 3 8 11 15 3. Time (seconds) 0 7 11 1 9. Time (seconds) 0 3 7 13 Altitude of balloon (meters) 50 1,0 1,0,00 3,30 Depth of sinking stone (meters) 3.51.77 5.9 7.9 8.73 Distance between Two Sleds (meters) 37.3 30. 7.7 0.8 7. Lesson -3 Chapter 17 Glencoe Algebra
-3 Stud Guide and Intervention Slope (continued) Slope m of a Line For points ( 1, 1 ) and (, ), where 1, m = change in change in = - 1-1 Eample 1 Find the slope of the line Eample that passes through (, -1) and (-, 5). m = - 1-1 = 5 - (-1) - - = - Slope formula = -1 Simplif. The slope of the line is -1. Eercises ( 1, 1 ) = (, -1), (, ) = (-, 5) Find two points on the line with integer coordinates, such as (1, ) and (3, -3). Divide the difference in the coordinates b the difference in the coordinates: -3 - () 3-1 = - 1 The slope of the line is - 1. Find the slope of the line. Find the slope of the line that passes through each pair of points. Epress as a fraction in simplest form. 1. (, 7) and (, 13). (, ) and (3, ) 3. (5, 1) and (7, -3). (5, -3) and (-, 3) 5. (5, 10) and (-1,). (-1, -) and (-13, ) 7. (7, ) and (3, 3) 8. (-5, 9) and (5, 5) 9. (, ) and (-, -8) Determine the rate of change of each graph. 10. 13. 11. 1. - - - 8-1. 15. - 8 - - Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 18 Glencoe Algebra
-3 Skills Practice Find the slope of the line that passes through each pair of points. 1. (1, 5), (-1, -3). (0, ), (3, 0) 3. (1, 9), (0, ). (8, -5), (, ) 5. (-3, 5), (-3, -1). (, ), (10, ) 7. (, 5), (, 7) 8. (, -), (3, ) 9. (5, ), (-3, ) Determine the rate of change of each graph. 10. 11. 1. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 13. 1. 15. Lesson -3 1. HIKING Naomi left from an elevation of 700 feet at 7:00 A.M. and hiked to an elevation of 9800 feet b 11:00 A.M. What was her rate of change in altitude? Chapter 19 Glencoe Algebra
-3 Practice Find the slope of the line that passes through each pair of points. Epress as a fraction in simplest form. 1. (3, -8), (-5, ). (-10, -3), (7, ) 3. (-7, -), (3, -). (8, ), (8, -1) 5. (, 3), (7, ). (-, -3), (-8, ) Determine the rate of change of each graph. 7. 8. - - - 9. 10. - 11. - 1. - - - 13. DEPRECIATION A machine that originall cost $15,00 has a value of $7500 at the end of 3 ears. The same machine has a value of $800 at the end of 8 ears. a. Find the average rate of change in value (depreciation) of the machine between its purchase and the end of 3 ears. - Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. b. Find the average rate of change in value of the machine between the end of 3 ears and the end of 8 ears. c. Interpret the sign of our answers. Chapter 0 Glencoe Algebra
-3 Word Problem Practice 1. TETHER A tether is tied tautl to the top of a pole as shown. What is the slope of the tether?. DESIGN An architect is designing a window with slanted interior bars. The crossbeam is perpendicular to the other four bars. What is the slope of the crossbeam? tether 9 ft Cross beam 1 ft 1 ft ft ft ft ft. AVIATION An airplane descends along a straight-line path with a slope of -0.1 to land at an airport. Use the information in the diagram to determine the initial height of the airplane. 5. READING The graph shows how man pages of her book Bridget read each da.? miles 10 10 Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 3. ROCK CLIMBING Gail is climbing at a popular rock climbing spot, Boulder Canon Sport Park in Colorado. The table below shows Gail s altitude above ground during a rock climb up a cliff. Time 50 miles Altitude (m) 10:00 0 10:0 10:0 30 11:00 33 Complete the following table of Gail s average rate of ascent. Pages Read 100 80 0 0 0 0 1 3 5 7 Da a. Find the average number of pages Bridget read per da. b. On which das did Bridget read more pages than her dail average? c. If Bridget had been able to keep up the pace she had on da 3, how man das would it have taken her to reach page 10? Lesson -3 Time Period Average rate of ascent (m/h) 10:00 10:0 10:0 10:0 10:0 11:00 Chapter 1 Glencoe Algebra
-3 Enrichment The Increase in Greenhouse Gases The atmosphere is composed of about 50% carbon dioide, CO. The level of carbon dioide is increasing due to increased fuel consumption and housing and commercial development. The concentration of a compound is measured in parts per million (ppm). For eample, if there were 500 CO molecules out of one million air particles, then the CO level would be 500 ppm. 1. In 195, the concentration of CO was 30 ppm. In 007, the concentration was 383 ppm. Determine the rate at which CO increased in ppm per ear.. Carbon dioide concentration is related to human consumption of fossil fuels and the decrease of trees due to development; therefore an increase in human population will result in an increase in carbon dioide. In 1980 the U.S. population was 5 million. The 000 census reported 81 million. At what rate is the population increasing per ear? What do ou estimate the U.S. population to be in 00? 3. Use the figures from Eercises 1 and to determine about how much CO is produced per million people in 011. Is it possible to reduce the concentration of carbon dioide in the atmosphere when the human population is increasing? Eplain.. The greenhouse effect is heat trapped b gases such as carbon dioide, which acts as a blanket for Earth. Higher concentration levels of carbon dioide amplif the greenhouse effect. Thus, global temperature is related to the concentration of CO. Records indicate that the increase in global temperature since 190 is 0.0 degrees Fahrenheit per ear. Each degree rise in temperature causes ocean levels to rise onehalf a foot. Use our data to determine in what ear the ocean level will rise feet. What impact will this have on coastal regions of the United States? Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Algebra