2. Welcome to Interactive Chalkboard Mathematics: Applications and Concepts, Course 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

3. Splash Screen

4. Contents Lesson 4-1Writing Expressions and Equations Lesson 4-2Solving Addition and Subtraction Equations Lesson 4-3Solving Multiplication Equations Lesson 4-4Solving Two-Step Equations Lesson 4-5Inequalities Lesson 4-6Functions and Linear Equations Lesson 4-7Lines and Slope

5. Lesson 1 Contents Example 1Write a Phrase as an Expression Example 2Write a Sentence as an Equation Example 3Write Sentences as Equations Example 4Write Sentences as Equations

6. Example 1-1a Write the phrase twenty dollars less the price of a movie ticket as an algebraic expression. twenty dollars less the price of a movie ticket Let m represent the price of a movie ticket. Answer: Words Variable Equation

7. Example 1-1b Write the phrase five more inches of snow than last year’s snowfall as an algebraic expression. Answer:

8. Example 1-2a Write the sentence a number less 4 is 12 as an algebraic equation. a number less 4 is 12 Let n represent a number. Answer: Words Variable Equation

9. Example 1-2b Write the sentence eight less than a number is 12 as an algebraic equation. Answer:

10. Example 1-3a Write the sentence twice a number is 18 as an algebraic equation. twice a number is 18 Let a represent a number. Answer: Words Variable Equation

11. Example 1-3b Write the sentence four times a number equals 96 as an algebraic equation. Answer:

12. Example 1-4a FOOD An average American adult drinks more soft drinks than any other beverage each year. Three times the number of gallons of soft drinks plus 27 is equal to the total 183 gallons of beverages consumed. Write an equation that models this situation. Three times the number of gallons of soft drinks plus 27 equals 183. Let s = the number of gallons of soft drinks. Answer: The equation is Words Variable Equation

13. Example 1-4b EXERCISE It is estimated that American adults spend an average of 8 hours per month exercising. This is 26 hours less than twice the number of hours spent watching television each month. Write an equation that models this situation. Answer:

14. End of Lesson 1

15. Lesson 2 Contents Example 1Solve an Addition Equation Example 2Solve a Subtraction Equation Example 3Use an Equation to Solve a Problem

16. Example 2-1a Solve Method 1 Use symbols. Write the equation. Subtract 14 from each side. Simplify.

17. Example 2-1b Method 2 Use models. Answer: The solution is 6.

18. Example 2-1b Solve Answer: –10

19. Example 2-2a Solve Check your solution. Method 1 Use symbols. Write the equation. Add 8 to each side. Simplify.

20. Example 2-2a Method 2 Use models.

21. Example 2-2a Check Write the original equation. Replace z with 20. This sentence is true. Answer: The solution is 20.

22. Example 2-2b Answer: Solve Check your solution.

23. Example 2-3a SPORTS If Tiger Woods had scores of –1, –4, and –3 on his first three rounds in a golf tournament, what would his fourth round score need to be if his final score was –18? The sum of the scores for all rounds was –18. Let s represent the score for the fourth round. scores for the first three rounds score for the fourth round final score Words Variable Equation

24. Example 2-3a Write the original equation. Add 8 to each side. Simplify. Check You can check the solution by adding. Answer: Tiger Woods needs to score –10 for the fourth round.

25. Example 2-3b HIKING Kyle wants to hike a trail that is 7 miles long. If he hikes 2, 1, and 2 miles during the first three hours of his hike, how far would he need to hike in the fourth hour in order to complete the trail? Answer:2 miles

26. End of Lesson 2

27. Lesson 3 Contents Example 1Solve Multiplication Equations Example 2Solve Multiplication Equations Example 3Use an Equation to Solve a Problem

28. Example 3-1a Solve Check your solution. Write the equation. Divide each side of the equation by 3. Check Write the original equation. Replace y with 13. Is this sentence true? Answer: The solution is 13.

29. Example 3-1b Answer: 7 Solve Check your solution.

30. Example 3-2a Solve Check your solution. Write the equation. Divide each side of the equation by –4. Check Write the original equation. Replace z with –15. Is this sentence true? Answer: The solution is –15.

31. Example 3-2b Answer: 4 Solve Check your solution.

32. Example 3-3a SPORTS At 6,072 feet, California Screamin’ is the longest steel roller coaster in the world. The ride takes 2 minutes 30 seconds to complete. Find the speed of the roller coaster in feet per second. Distance is equal to rate times the time. d r t 6,072r 150 Words Variable Equation

33. Example 3-3a Write the equation. Divide each side of the equation by 150. Answer: The roller coaster travels at a speed of 40.48 feet per second.

34. Example 3-3b TRAVEL David is driving on a business trip. He drives a total of 589 miles at an average speed of 62 miles per hour. How many hours does David spend driving? Answer: 9.5 hours

35. End of Lesson 3

36. Lesson 4 Contents Example 1Solve a Two-Step Equation Example 2Solve a Two-Step Equation Example 3Solve a Two-Step Equation Example 4Use an Equation to Solve a Problem

37. Example 4-1a Solve Check your solution. Write the equation. Subtract 3 from each side. Simplify. Divide each side by 4. Simplify.

38. Example 4-1a Write the original equation. Replace x with 4. Is this sentence true? Answer: The solution is 4. Check

39. Example 4-1b Answer: 7 Solve Check your solution.

40. Example 4-2a Solve. Check your solution. Write the equation. Subtract 9 from each side. Simplify. Divide each side by –3. Simplify.

41. Example 4-2a Write the original equation. Replace c with 2. Is this sentence true? Answer: The solution is 2. Check

42. Example 4-2b Answer: –3 Solve. Check your solution.

43. Example 4-3a Write the equation. Subtract 6 from each side. Simplify. Divide each side by 3. Simplify. Solve Check your solution.

44. Example 4-3a Write the original equation. Replace t with –2. Is this sentence true? Answer: The solution is –2. Check

45. Example 4-3b Answer: 8 Solve Check your solution.

46. Example 4-4a PARKS There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi? Three times the number of acres of state parkland in Mississippi plus 4,000 equals 76,000. Let m the acres of state parkland in Mississippi. Words Variable Equation

47. Example 4-4a Answer: There are 24,000 acres of state parkland in Mississippi. Write the equation. Subtract 4,000 from each side. Simplify. Divide each side by 3. Simplify.

48. Example 4-4b BASEBALL Matthew had 64 hits during last year’s baseball season. This was 8 less than twice the number of hits Gregory had. How many hits did Gregory have during last year’s baseball season? Answer: 36 hits

49. End of Lesson 4

50. Lesson 5 Contents Example 1Graph Solutions of Inequalities Example 2Graph Solutions of Inequalities Example 3Graph Solutions of Inequalities Example 4Graph Solutions of Inequalities Example 5Solve One-Step Inequalities Example 6Solve One-Step Inequalities Example 7Use an Inequality to Solve a Problem

51. Example 5-1a Graph the inequality on a number line. The open circle means that the number is not included in the solution. Answer:

52. Example 5-1b Graph the inequality on a number line. Answer:

53. Example 5-2a Graph the inequality on a number line. The closed circle means that the number is included in the solution. Answer:

54. Example 5-2b Graph the inequality on a number line. Answer:

55. Example 5-3a Graph the inequality on a number line. Answer:

56. Example 5-3b Graph the inequality on a number line. Answer:

57. Example 5-4a Graph the inequality on a number line. Answer:

58. Example 5-4b Graph the inequality on a number line. Answer:

59. Example 5-5a Write the inequality. Add 7 to each side. Simplify. Solve Check your solution. Then graph the solution.

60. Example 5-5a Check Try 8, a number less than 9. Write the inequality. Replace x with 8. Is this sentence true? Answer: The solution is all numbers less than 9.

61. Example 5-5b Answer: Solve Check your solution. Then graph the solution.

62. Example 5-6a Write the inequality. Divide each side by 6. Check this solution. Answer: The solution is all numbers greater than or equal to 4. Solve Graph the solution.

63. Example 5-6b Solve Graph the solution. Answer:

64. Example 5-7a BASEBALL CARDS Jacob is buying uncirculated baseball cards online. The cards he has chosen are $6.70 each and the Web site charges a $1.50 service charge for each sale. If Jacob has no more than $35 to spend, how many cards can he buy? Let c represent the number of baseball cards Jacob can buy. Write the inequality. Subtract 1.50 from each side. Simplify.

65. Example 5-7b Divide each side by 6.70. Answer: Jacob can buy no more than 5 baseball cards.

66. Example 5-7c BOWLING Danielle is going bowling. The charge for renting shoes is $1.25 and each game costs $2.25. If Danielle has no more than $8 to spend on bowling, how many games can she play? Answer: no more than 3

67. End of Lesson 5

68. Lesson 6 Contents Example 1Make a Function Table Example 2Graph Solutions of Linear Equations Example 3Represent Real-World Functions

69. Example 6-1a WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’s total earnings for working 1, 2, 3, and 4 hours. InputFunctionOutput Number of Hours Multiply by 6 Total Earnings ($) 6 6  1 1 12 6  2 2 18 6  3 3 24 6  4 4

70. Example 6-1b MOVIE RENTAL Dave goes to the video store to rent a movie. The cost per movie is $3.50. Make a function table that shows the amount Dave would pay for renting 1, 2, 3, and 4 movies. Input Function RuleOutput Number of Movies Multiply by 3.50 Total Cost ($) 1 3.50  1 3.50 2 3.50  2 7.00 3 3.50  3 10.50 4 3.50  4 14.00 Answer:

71. Example 6-2a Graph Select any four values for the input x. We chose 2, 1, 0, and –1. Substitute these values for x to find the output y. Answer: Four solutions are (2, 5), (1, 4), (0, 3), and (–1, 2). (2, 5) (1, 4) (0, 3) (–1, 2)

72. Example 6-2b Answer: Graph

73. Example 6-3a ANIMALS Blue whales can reach a speed of 30 miles per hour in bursts when in danger. The equation describes the distance d that a whale traveling at that speed can travel in time t. Represent this function with a graph. Step 1Select any four values for t. Select only positive numbers because t represents time. Make a function table. t30td(t, d) 230(2) 60(2, 60) 330(3) 90(3, 90) 530(5)150(5, 150) 630(6)180(6, 180)

74. Example 6-3b Step 2Graph the ordered pairs and draw a line through the points. Answer:

75. Example 6-3c TRAVEL Susie takes a car trip traveling at an average speed of 55 miles per hour. The equation describes the distance d that Susie travels in time t. Represent this function with a graph. Answer:

76. End of Lesson 6

77. Lesson 7 Contents Example 1Positive Slope Example 2Negative Slope Example 3Negative Slope Example 4Compare Slopes

78. Example 7-1a Find the slope of the line. 4 units up 2 units right Answer: The slope of the line is 2.

79. Example 7-1b Find the slope of the line. Answer:

80. Example 7-2a Find the slope of the line. Answer: The slope of the line is –1. 5 units up 5 units left

81. Example 7-2b Find the slope of the line. Answer: –2

82. Example 7-3a Find the slope of the line. Answer: The slope of the line is 3 units down 4 units right

83. Example 7-3b Find the slope of the line. Answer:

84. Example 7-4a A rise: 30 in.; run: 300 in. B rise: 30 in.; run: 360 in. C rise: 30 in.; run: 380 in. D rise: 30 in.; run: 400 in. MULTIPLE- CHOICE TEST ITEM The Americans with Disabilities Act states that the maximum slope of a ramp in new construction shall be. Which ramp does not meet this requirement?

85. Example 7-4a Read the Test Item The rise corresponds to the vertical change, or change in y. The run corresponds to the horizontal change, or change in x. Solve the Test Item Find the slope of each ramp.

86. Example 7-4a Answer: A The only ramp with a slope greater than is Ramp A.

87. Example 7-4b A rise: 50 ft; run: 700 ft B rise: 30 ft; run: 420 ft C rise: 40 ft; run: 480 ft D rise: 60 ft; run: 840 ft MULTIPLE- CHOICE TEST ITEM The architects building a new baseball stadium want all of the ramps in the stadium to have the same slope. Which of the following ramps has a different slope from the others? Answer: C

88. End of Lesson 7

89. Online Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Mathematics: Applications and Concepts, Course 2 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.msmath2.net/extra_examples.

90. Transparency 1 Click the mouse button or press the Space Bar to display the answers.

91. Transparency 1a

92. Transparency 2 Click the mouse button or press the Space Bar to display the answers.

93. Transparency 2a

94. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

95. Transparency 3a

96. Transparency 4 Click the mouse button or press the Space Bar to display the answers.

97. Transparency 4a

98. Transparency 5 Click the mouse button or press the Space Bar to display the answers.

99. Transparency 5a

100. Transparency 6 Click the mouse button or press the Space Bar to display the answers.

101. Transparency 6a

102. Transparency 7 Click the mouse button or press the Space Bar to display the answers.

103. Transparency 7a

104. Help To navigate within this Interactive Chalkboard product: Click the Forward button to go to the next slide. Click the Previous button to return to the previous slide. Click the Section Back button to return to the beginning of the lesson you are working on. If you accessed a feature, this button will return you to the slide from where you accessed the feature. Click the Main Menu button to return to the presentation main menu. Click the Help button to access this screen. Click the Exit button or press the Escape key [Esc] to end the current slide show. Click the Extra Examples button to access additional examples on the Internet. Click the 5-Minute Check button to access the specific 5-Minute Check transparency that corresponds to each lesson.

105. End of Custom Show End of Custom Shows WARNING! Do Not Remove This slide is intentionally blank and is set to auto-advance to end custom shows and return to the main presentation.

106. End of Slide Show