Welcome to Interactive Chalkboard Algebra 1 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Welcome to Interactive Chalkboard

Splash Screen

Lesson 5-2 Slope and Direct Variation Lesson 5-3 Slope-Intercept Form Lesson 5-4 Writing Equations in Slope-Intercept Form Lesson 5-5 Writing Equations in Point-Slope Form Lesson 5-6 Geometry: Parallel and Perpendicular Lines Lesson 5-7 Statistics: Scatter Plots and Lines of Fit Contents

Example 1 Positive Slope Example 2 Negative Slope Example 3 Zero Slope Example 4 Undefined Slope Example 5 Find Coordinates Given Slope Example 6 Find a Rate of Change Lesson 1 Contents

Find the slope of the line that passes through (–3, 2) and (5, 5). Let and Substitute. Example 1-1a

Simplify. Answer: The slope is Example 1-1b

Find the slope of the line that passes through (4, 5) and (7, 6). Answer: Example 1-1c

Find the slope of the line that passes through (–3, –4) and (–2, –8). Let and Substitute. Example 1-2a

Simplify. Answer: The slope is –4. Example 1-2b

Find the slope of the line that passes through (–3, –5) and (–2, –7). Answer: –2 Example 1-2c

Find the slope of the line that passes through (–3, 4) and (4, 4). Let and Substitute. Example 1-3a

Simplify. Answer: The slope is 0. Example 1-3b

Find the slope of the line that passes through (–3, –1) and (5, –1). Answer: 0 Example 1-3c

Find the slope of the line that passes through (–2, –4) and (–2, 3). Let and Answer: Since division by zero is undefined, the slope is undefined. Example 1-4a

Find the slope of the line that passes through (5, –1) and (5, –3). Answer: undefined Example 1-4b

Find the value of r so that the line through (6, 3) and (r, 2) has a slope of Slope formula Substitute. Subtract. Example 1-5a

Find the cross products. Simplify. Add 6 to each side. Answer: Simplify. Example 1-5b

Find the value of p so that the line through (p, 4) and (3, –1) has a slope of Answer: –5 Example 1-5c

Find the rates of change for 1991-1995 and 1995-1999. Travel The graph to the right shows the number of U.S. passports issued in 1991, 1995, and 1999. Find the rates of change for 1991-1995 and 1995-1999. Use the formula for slope. millions of passports years Example 1-6a

1991-1995: Substitute. Simplify. Answer: The number of passports issued increased by 1.9 million in a 4-year period for a rate of change of 475,000 per year. Example 1-6b

1995-1999: Substitute. Simplify. Answer: Over this 4-year period, the number of U.S. passports issued increased by 1.4 million for a rate of change of 350,000 per year. Example 1-6c

Explain the meaning of slope in each case. Answer: For 1991-1995, on average, 475,000 more passports were issued each year than the last. For 1995-1999, on average, 350,000 more passports were issued each year than the last. Example 1-6d

How are the different rates of change shown on the graph? Answer: There is a greater rate of change from 1991-1995 than from 1995-1999. Therefore, the section of the graph for 1991-1995 has a steeper slope. Example 1-6e

a. Find the rates of change for 1990-1995 and 1995-2000. Airlines The graph shows the number of airplane departures in the United States in recent years. a. Find the rates of change for 1990-1995 and 1995-2000. Answer: 240,000 per year; 180,000 per year Example 1-6f

b. Explain the meaning of the slope in each case. Answer: For 1990-1995, the number of airplane departures increased by about 240,000 flights each year. For 1995-2000, the number of airplane departures increased by about 180,000 flights each year. Example 1-6g

c. How are the different rates of change shown on the graph? Answer: There is a greater vertical change for 1990-1995 than for 1995-2000. Therefore, the section of the graph for 1990-1995 has a steeper slope. Example 1-6h

End of Lesson 1

Example 1 Slope and Constant of Variation Example 2 Direct Variation with k > 0 Example 3 Direct Variation with k < 0 Example 4 Write and Solve a Direct Variation Equation Example 5 Direct Variation Equation Lesson 2 Contents

Answer: The constant of variation is 2. The slope is 2. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. Slope formula Answer: The constant of variation is 2. The slope is 2. Simplify. Example 2-1a

Answer: The constant of variation is –4. The slope is –4. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. Slope formula Answer: The constant of variation is –4. The slope is –4. Simplify. Example 2-1b

Answer: constant of variation: 4; slope: 4 Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. a. Answer: constant of variation: 4; slope: 4 Example 2-1c

Answer: constant of variation: –3; slope: –3 Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. b. Answer: constant of variation: –3; slope: –3 Example 2-1d

Step 1 Write the slope as a ratio. Step 2 Graph (0, 0). Step 3 From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot. Step 4 Draw a line containing the points. Example 2-2a

Answer: Example 2-2b

Step 1 Write the slope as a ratio. Step 2 Graph (0, 0). Step 3 From the point (0, 0), move down 3 units and right 2 units. Draw a dot. Step 4 Draw a line containing the points. Example 2-3a

Answer: Example 2-3b

Suppose y varies directly as x, and when Write a direct variation equation that relates x and y. Find the value of k. Direct variation formula Replace y with 9 and x with –3. Divide each side by –3. Example 2-4a

Simplify. Answer: Therefore, Example 2-4b

Use the direct variation equation to find x when Replace y with 15. Divide each side by –3. Simplify. Answer: Therefore, when Example 2-4c

Suppose y varies directly as x, and when a. Write a direct variation equation that relates x and y. b. Use the direct variation equation to find x when Answer: Answer: –15 Example 2-4d

Travel The Ramirez family is driving cross-country on vacation Travel The Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours. Write a direct variation equation to find the distance driven for any number of hours. Words The distance traveled is 330 miles, and the time is 5.5 hours. Variables Distance equals rate times time. Equation 330 mi r 5.5h Example 2-5a

Answer: Therefore, the direct variation equation is Solve for the rate. Original equation Divide each side by 5.5. Simplify. Answer: Therefore, the direct variation equation is Example 2-5b

The graph of passes through the origin with a slope of 60. Graph the equation. The graph of passes through the origin with a slope of 60. Answer: Example 2-5c

Estimate how many hours it would take to drive 600 miles. Original equation Replace d with 600. Divide each side by 60. Simplify. Answer: At this rate, it will take 10 hours to drive 600 miles. Example 2-5d

Dustin ran a 26-mile marathon in 3.25 hours. a. Write a direct variation equation to find the distance ran for any number of hours. b. Graph the equation. Answer: Answer: Example 2-5e

c. Estimate how many hours it would take to jog 16 miles. Answer: 2 hours Example 2-5f

End of Lesson 2

Example 1 Write an Equation Given Slope and y-Intercept Example 2 Write an Equation Given Two Points Example 3 Graph an Equation in Slope-Intercept Form Example 4 Graph an Equation in Standard Form Example 5 Write an Equation in Slope-Intercept Form Lesson 3 Contents

Replace m with and b with –6. Write an equation of the line whose slope is and whose y-intercept is –6. Slope-intercept form Replace m with and b with –6. Answer: Example 3-1a

Write an equation of the line whose slope is 4 and whose y-intercept is 3. Answer: Example 3-1b

Write an equation of the line shown in the graph. Step 1 You know the coordinates of two points on the line. Find the slope. Let Example 3-2a

Step 3 Finally, write the equation. Simplify. The slope is 2. Step 2 The line crosses the y-axis at (0, –3). So, the y-intercept is –3. Step 3 Finally, write the equation. Slope-intercept form Replace m with 2 and b with –3. Answer: The equation of the line is Example 3-2b

Write an equation of the line shown in the graph. Answer: Example 3-2c

Step 1 The y-intercept is –7. So graph (0, –7). y = 0.5x – 7 Step 2 The slope is 0.5 or From (0, –7), move up 1 unit and right 2 units. Draw a dot. Step 3 Draw a line connecting the points. Example 3-3a

Graph Answer: Example 3-3b

Step 1 Solve for y to find the slope-intercept form. Graph Step 1 Solve for y to find the slope-intercept form. Original equation Subtract 5x from each side. Simplify. Divide each side by 4. Example 3-4a

Divide each term in the numerator by 4. Answer: Step 2 The y-intercept of is 2. So graph (0, 2). Example 3-4b

From (0, 2), move down 5 units and right 4 units. Draw a dot. Step 3 The slope is From (0, 2), move down 5 units and right 4 units. Draw a dot. 5x + 4y = 8 Step 4 Draw a line connecting the points. Example 3-4c

Graph Answer: Example 3-4d

Health The ideal maximum heart rate for a 25-year-old who is exercising to burn fat is 117 beats per minute. For every 5 years older than 25, that ideal rate drops 3 beats per minute. Write a linear equation to find the ideal maximum heart rate for anyone over 25 who is exercising to burn fat. Words The rate drops 3 beats per minute every 5 years, so the rate of change is beats per minute each year. The ideal maximum heart rate for a 25-year-old is 117 beats per minute. Example 3-5a

R a 117 Variables Let R = the ideal heart rate. Let a = years older than 25. Equation ideal rate Ideal rate of years older for 25- rate equals change times than 25 plus year-old. R a 117 Answer: Example 3-5b

The graph passes through (0, 117) with a slope of Graph the equation. The graph passes through (0, 117) with a slope of Answer: Example 3-5c

The age 55 is 30 years older than 25. So, Find the ideal maximum heart rate for a person exercising to burn fat who is 55 years old. The age 55 is 30 years older than 25. So, Ideal heart rate equation Replace a with 30. Simplify. Answer: The ideal heart rate for a 55-year-old person is 99 beats per minute. Example 3-5d

The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986. a. Write a linear equation to find the average amount spent for any year since 1986. Answer: where D is the amount of money spent in millions of dollars, and n is the number of years since 1986 Example 3-5e

The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986. b. Graph the equation. Answer: Example 3-5f

c. Find the amount spent by consumers in 1999. The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986. c. Find the amount spent by consumers in 1999. Answer: $4.95 million Example 3-5g

End of Lesson 3

Example 1 Write an Equation Given Slope and One Point Example 2 Write an Equation Given Two Points Example 3 Write an Equation to Solve a Problem Example 4 Linear Extrapolation Lesson 4 Contents

Write an equation of a line that passes through (2, –3) with slope Step 1 The line has slope To find the y-intercept, replace m with and (x, y) with (2, –3) in the slope-intercept form. Then, solve for b. Example 4-1a

Replace m with , y with –3, and x with 2. Slope-intercept form Replace m with , y with –3, and x with 2. Multiply. Subtract 1 from each side. Simplify. Example 4-1b

Step 2 Write the slope-intercept form using Replace m with and b with –4. Answer: The equation is Example 4-1c

Check You can check your result by graphing on a graphing calculator. Use the CALC menu to verify that it passes through (2, –3). Example 4-1d

Write an equation of a line that passes through (1, 4) and has a slope of –3. Answer: Example 4-1e

x y –3 –4 –2 –8 Multiple-Choice Test Item The table of ordered pairs shows the coordinates of two points on the graph of a function. Which equation describes the function? A B C D x y –3 –4 –2 –8 Read the Test Item The table represents the ordered pairs (–3, –4) and (–2, –8). Example 4-2a

Step 1 Find the slope of the line containing the points. Let and . Solve the Test Item Step 1 Find the slope of the line containing the points. Let and . Slope formula Simplify. Example 4-2b

Replace m with –4, x with –3, and y with –4. Step 2 You know the slope and two points. Choose one point and find the y-intercept. In this case, we chose (–3, –4). Slope-intercept form Replace m with –4, x with –3, and y with –4. Multiply. Subtract 12 from each side. Simplify. Example 4-2c

Step 3 Write the slope-intercept form using Replace m with –4 and b with –16. Answer: The equation is The answer is D. Example 4-2d

x y –1 3 2 6 Multiple-Choice Test Item The table of ordered pairs shows the coordinates of two points on the graph of a function. Which equation describes the function? A B C D x y –1 3 2 6 Answer: B Example 4-2e

Explore You know the cost of regular gasoline in May and June. Economy In 2000, the cost of many items increased because of the increase in the cost of petroleum. In Chicago, a gallon of self-serve regular gasoline cost $1.76 in May and $2.13 in June. Write a linear equation to predict the cost of gasoline in any month in 2000, using 1 to represent January. Explore You know the cost of regular gasoline in May and June. Plan Let x represent the month and y represent the cost of gasoline that month. Write an equation of the line that passes through (5, 1.76) and (6, 2.13). Example 4-3a

Solve Find the slope. Slope formula Let and . Simplify. Example 4-3b

Choose (5, 1.76) and find the y-intercept of the line. Slope-intercept form Replace m with 0.37, x with 5, and y with 1.76. Multiply. Subtract 1.85 from each side. Simplify. Example 4-3c

Write the slope-intercept form using and Replace m with 0.37 and b with –0.09. Answer: The equation is Example 4-3d

Replace y with 2.13 and x with 6. Examine Check your result by substituting the coordinates of the point not chosen, (6, 2.13), into the equation. Original equation Replace y with 2.13 and x with 6. Multiply. Simplify. Example 4-3e

The average cost of a college textbook in 1997 was $57. 65 The average cost of a college textbook in 1997 was $57.65. In 2000, the average cost was $68.15. Write a linear equation to estimate the average cost of a textbook in any given year since 1997. Let x represent years since 1997. Answer: Example 4-3f

Economy The Yellow Cab Company budgeted $7000 for the July gasoline supply. On average, they use 3000 gallons of gasoline per month. Use the prediction equation where x represents the month and y represents the cost of one gallon of gasoline, to determine if they will have to add to their budget. Explain. Original equation Replace x with 7. Simplify. Example 4-4a

Answer: If gas increases at the same rate, a gallon of gasoline will cost $2.50 in July. 3000 gallons at this price is $7500, so they will have to add $500 to their budget. Example 4-4b

A student is starting college in 2004 and has saved $400 to use for textbooks. Use the prediction equation where x is the years since 1997 and y is the average cost of a college textbook, to determine whether they will have enough money for 5 textbooks. Answer: If the cost of textbooks increases at the same rate, the average cost will be $82.15 in 2004. Five textbooks at this price is $410.75, so he will not have enough money. Example 4-4c

End of Lesson 4

Example 1 Write an Equation Given Slope and a Point Example 2 Write an Equation of a Horizontal Line Example 3 Write an Equation in Standard Form Example 4 Write an Equation in Slope-Intercept Form Example 5 Write an Equation in Point-Slope Form Lesson 5 Contents

Answer: The equation is Write the point-slope form of an equation for a line that passes through (–2, 0) with slope Point-slope form Simplify. Answer: The equation is Example 5-1a

Write the point-slope form of an equation for a line that passes through (4, –3) with slope –2. Answer: Example 5-1b

Answer: The equation is Write the point-slope form of an equation for a horizontal line that passes through (0, 5). Point-slope form Simplify. Answer: The equation is Example 5-2a

Write the point-slope form of an equation for a horizontal line that passes through (–3, –4). Answer: Example 5-2b

Multiply each side by 4 to eliminate the fraction. Write in standard form. In standard form, the variables are on the left side of the equation. A, B, and C are all integers. Original equation Multiply each side by 4 to eliminate the fraction. Distributive Property Example 5-3a

Subtract 3x from each side. Simplify. Answer: The standard form of the equation is Example 5-3b

Write in standard form. Answer: Example 5-3c

Write in slope-intercept form. In slope-intercept form, y is on the left side of the equation. The constant and x are on the right side. Original equation Distributive Property Add 5 to each side. Example 5-4a

Answer: The slope-intercept form of the equation is Simplify. Answer: The slope-intercept form of the equation is Example 5-4b

Write in slope-intercept form. Answer: Example 5-4c

The figure shows trapezoid ABCD with bases and Write the point-slope form of the lines containing the bases of the trapezoid. Example 5-5a

Step 1 First find the slopes of and Slope formula Slope formula Example 5-5b

Step 2 You can use either point for (x1, y1) in the point-slope form. Method 1 Use (–2, 3). Method 2 Use (4, 3). Example 5-5c

Method 1 Use (1, –2). Method 2 Use (6, –2). Answer: The point-slope form of the equation containing The point-slope form of the equation containing Example 5-5d

Write each equation in standard form. Original equation Add 3 to each side. Answer: Simplify. Original equation Subtract 2 from each side. Answer: Simplify. Example 5-5e

The figure shows right triangle ABC. a. Write the point-slope form of the line containing the hypotenuse b. Write the equation in standard form. Answer: Answer: Example 5-5f

End of Lesson 5

Example 1 Parallel Line Through a Given Point Example 2 Determine Whether Lines are Perpendicular Example 3 Perpendicular Line Through a Given Point Example 4 Perpendicular Line Through a Given Point Lesson 6 Contents

Write the slope-intercept form of an equation for the line that passes through (4, –2) and is parallel to the graph of The line parallel to has the same slope, Replace m with and (x, y) with (4, -2) in the point-slope form. Example 6-1a

Replace m with y with –2, and x with 4. Point-slope form Replace m with y with –2, and x with 4. Simplify. Distributive Property Subtract 2 from each side. Example 6-1b

Write the equation in slope-intercept form. Answer: The equation is Example 6-1c

Check. You can check your result by graphing both equations Check You can check your result by graphing both equations. The lines appear to be parallel. The graph of passes through (4, –2). Example 6-1d

Write the slope-intercept form of an equation for the line that passes through (2, 3) and is parallel to the graph of Answer: Example 6-1e

Geometry The height of a trapezoid is measured on a segment that is perpendicular to a base. In trapezoid ARTP, and are bases. Can be used to measure the height of the trapezoid? Explain. Example 6-2a

Find the slope of each segment. Example 6-2b

Answer: The slope of. and. is 1 and the slope of Answer: The slope of and is 1 and the slope of is not perpendicular to and , so it cannot be used to measure height. Example 6-2c

The graph shows the diagonals of a rectangle The graph shows the diagonals of a rectangle. Determine whether is perpendicular to Answer: The slope of is and the slope of is Since is not perpendicular to Example 6-2d

Step 1 Find the slope of the given line. Write the slope-intercept form for an equation of a line that passes through (4, –1) and is perpendicular to the graph of Step 1 Find the slope of the given line. Original equation Subtract 7x from each side. Simplify. Example 6-3a

Divide each side by –2. Simplify. Step 2 The slope of the given line is So, the slope of the line perpendicular to this line is the opposite reciprocal of or Example 6-3b

Step 3 Use the point-slope form to find the equation. and Simplify. Distributive Property Example 6-3c

Subtract 1 from each side. Simplify. Answer: The equation of the line is Example 6-3d

Check You can check your result by graphing both equations on a graphing calculator. Use the CALC menu to verify that passes through (4, –1). Example 6-3e

Write the slope-intercept form for an equation of a line that passes through (–3, 6) and is perpendicular to the graph of Answer: Example 6-3f

Subtract 5x from each side. Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through (0, 6). Step 1 Find the slope of Original equation Subtract 5x from each side. Simplify. Example 6-4a

Divide each side by 2. Simplify. Step 2 The slope of the given line is So, the slope of the line perpendicular to this line is the opposite reciprocal of or Example 6-4b

Replace x1 with 0, y1 with 6, and m with Step 3 Substitute the slope and the given point into the point-slope form of a linear equation. Then write the equation in slope-intercept form. Point-slope form Replace x1 with 0, y1 with 6, and m with Distributive Property Answer: The equation of the line is Example 6-4c

Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through the x-intercept of that line. Answer: Example 6-4d

End of Lesson 6

Example 1 Analyze Scatter Plots Example 2 Find a Line of Fit Example 3 Linear Interpolation Lesson 7 Contents

The graph shows average personal income for U.S. citizens. Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. The graph shows average personal income for U.S. citizens. Answer: The graph shows a positive correlation. With each year, the average personal income rose. Example 7-1a

Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. The graph shows the average students per computer in U.S. public schools. Answer: The graph shows a negative correlation. With each year, more computers are in the schools, making the students per computer rate smaller. Example 7-1b

a. The graph shows the number of mail-order prescriptions. Determine whether each graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. a. The graph shows the number of mail-order prescriptions. Answer: Positive correlation; with each year, the number of mail-order prescriptions has increased. Example 7-1c

Answer: no correlation Determine whether each graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. b. The graph shows the percentage of voter participation in Presidential Elections. Answer: no correlation Example 7-1d

Population (millions) The table shows the world population growing at a rapid rate. Year Population (millions) 1650 500 1850 1000 1930 2000 1975 4000 1998 5900 Example 7-2a

Draw a scatter plot and determine what relationship exists, if any, in the data. Let the independent variable x be the year and let the dependent variable y be the population (in millions). The scatter plot seems to indicate that as the year increases, the population increases. There is a positive correlation between the two variables. Example 7-2b

Draw a line of fit for the scatter plot. No one line will pass through all of the data points. Draw a line that passes close to the points. A line is shown in the scatter plot. Example 7-2c

Write the slope-intercept form of an equation for equation for the line of fit. The line of fit shown passes through the data points (1850, 1000) and (1998, 5900). Step 1 Find the slope. Slope formula Let and Simplify. Example 7-2d

Answer: The equation of the line is . Step 2 Use m = 33.1 and either the point-slope form or the slope-intercept form to write the equation. You can use either data point. We chose (1850, 1000). Point-slope form Slope-intercept form Answer: The equation of the line is . Example 7-2e

Check Check your result by substituting (1998, 5900) into Line of fit equation Replace x with 1998 and y with 5900. Multiply. Subtract. The solution checks. Example 7-2f

The table shows the number of bachelor’s degrees received since 1988. Years Since 1988 2 4 6 8 10 Bachelor’s Degrees Received (thousands) 1051 1136 1169 1165 1184 Source: National Center for Education Statistics Example 7-2g

a. Draw a scatter plot and determine what relationship exists, if any, in the data. Answer: The scatter plot seems to indicate that as the number of years increase, the number of bachelor’s degrees received increases. There is a positive correlation between the two variables. Example 7-2h

b. Draw a line of best fit for the scatter plot. c. Write the slope-intercept form of an equation for the line of fit. Answer: Using (4, 1137) and (10, 1184), Example 7-2i

Use the prediction equation where x is the year and y is the population (in millions), to predict the world population in 2010. Original equation Replace x with 2010. Simplify. Answer: 6,296,000,000 Example 7-2a

Use the equation where x is the years since 1988 and y is the number of bachelor’s degrees (in thousands), to predict the number of bachelor’s degrees that will be received in 2005. Answer: 1,204,000 Example 7-3b

End of Lesson 7

Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Algebra 1 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.algebra1.com/extra_examples. Algebra1.com

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

Transparency 1a

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

Transparency 2a

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

Transparency 3a

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

Transparency 4a

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

Transparency 5a

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

Transparency 6a

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

Transparency 7a

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. End of Custom Show

End of Slide Show