Answers for the lesson Write Linear Equations in Slope-Intercept Form

(1)

Skill Practice 1. slope

2. You can substitute the slope for m and the y-intercept for b to get the equation of the line.

3. y 5 2x 1 9 ^4. y 5 x 1 5

5. y 5 23x ^6. y 5 27x 1 1

7. y 5 ²^}₃ x 2 9 8. y 5 ^}³₄ x 2 6

9. A

10. y 5 x 2 4 ^11. y 5 2 ^}¹₂ x

12. y 5 23x 1 4

13. y 5 ²^}₃ x 2 8

14. y 5 2x 2 3 15. y 5 22x 2 2

16. The given slope and y-intercept were interchanged in the slope- intercept form of the equation;

y 5 2x 1 7.

17. The slope should be ^}^{0 2 4}_{5 2 0} , y 5 2 ^}⁴₅ x 1 4.

18. y 5 ¹^}₃ x 1 2 19. y 5 4x 1 4

20. y 5 2 ^}¹₄ x 1 3

21. y 5 2 ^}⁴₃ x

22. y 5 x 2 4 23. y 5 2x 2 2

24. y 5 23x 2 8

25. y 5 2x 2 5

26. y 5 24

27. y 5 20.0625x 1 4

28. y 5 2 ^}⁸₃ x 1 5

29. y 5 24x 2 24

30. y 5 x 1 2 31. y 5 22x 1 7

32. y 5 2 ^}¹₄ x 2 2

33. y 5 2 ^}⁴₅ x 2 1

34. y 5 25x 2 4

35. y 5 ^}²₃ x 1 3

36. y 5 22x 1 21

37. y 5 23x 1 9

38. y 5 2x 1 0.6

39. The equations in slope-intercept form of the two lines are k:

y 5 2x 2 1 and l: y 5 2 } ¹3 x 1 1.

The parameter m changed from 2 to 2 ¹} 3 and the parameter b changed from 21 to 1.

40. Sample answer: A health club offers an aerobics membership that charges $9 plus $4 per class.

41. y 5 22x 1 1

Answers for the lesson “Write Linear Equations in Slope-Intercept Form”

LESSON

4.1

(2)

42. y 5 ¹^}₂ x

43. No; the slope of the line is undefined, the equation is x 5 3, which is not in slope- intercept form.

44. Find the slope by substituting the values: ^{b 1 m 2 b}^}_{1 2 0} 5 m. The y-intercept is when x 5 0, so the y-intercept is b. If you substitute (21, b 2 m) into the equation y 5 mx 1 b, you get

b 2 m 5 2m 1 b which is a true statement.

Problem Solving 45. a. C 5 44m 1 48

b. $312

46. C 5 3.99e 1 1.49; $33.41

47. C 5 3h 1 30; $42

48. a. a 5 0.0037e 1 3

b. dependent variable: a, independent variable: e

c. Substitute 2 for e to get approximately 3.

49. a. x (years

since 1970) y

(

km²

)

0 5.2

10 4.1

b.

10

0 20 30

6 5 4 3 2 1

0 !

"

The area of the glaciers changed 21.1 square kilometers between every 10 year interval.

c. y 5 20.11x 1 5.2; 20.11 km²

50. a. 81 million gal

b. y 5 130,000,000h

c. 0b h b 3; water is only released for 3 hours after 10 ^A.^M.

51. a. t 5 0.7d 1 2 ^b. 16 min

52. a. d 5 ^}₁₀₀₀⁷ e 1 400

b. d ft 5 ^}₁₀₀₀⁷ + e ft 1 400 ft

c. 424.5 ft

(3)

Skill Practice 1. y-intercept

2. It is the point where x is 0.

3. y 5 3x 2 2 4. y 5 2x 2 9

5. y 5 25x 2 13

6. y 5 22x 1 5

7. y 5 2 ^}³₄ x 1 2 8. y 5 ^}¹₂ x 2 ¹⁹^}₂

9. 23 was substituted for x instead of y and 6 was substituted for y instead of x, 23 5 22(6) 1 b, 23 5 212 1 b, 9 5 b.

10. 18 should have been substituted for m, not b, 81 5 (18)2 1 b, 81 5 36 1 b, b 5 $45.

11. y 5 3x 1 1 12. y 5 7x 2 19

13. y 5 2 ^}²₅ x 2 1

14. y 5 2x 1 12

15. y 5 2 ^}³₄ x 1 ³⁵^}₈

16. y 5 2 ^}¹₂ x 2 ⁷^}₄

17. y 5 4x 2 15 18. y 5 ^}²₅ x 1 ⁴^}₅

19. y 5 2 ^}¹₂ x 1 ¹^}₂

20. y 5 2 ^}⁷₆ x 1 ¹¹^}₆

21. y 5 ¹^}₃ x 2 ^}⁴₃ 22. y 5 23x 2 7

23. y 5 22x 1 11

24. y 5 2x 2 4

25. y 5 2 ^}¹₂ x 1 8

26. y 5 ^}³₄ x 2 5

27. y 5 x 2 2 28. y 5 23x 2 6

29. D

30. y 5 2 ^}¹₄ x 1 5

31. y 5 2 ^}²₃ x 1 6

32. y 5 2 ^}¹₂ x 1 3

33. y 5 6x 2 4

34. Yes; you can find the slope and then substitute m and the coordinates of the point in y 5 mx 1 b, solve for b, and write the equation.

35. Yes; you can substitute m and the coordinates of the point in y 5 mx 1 b, solve for b, and write the equation.

36. No; many lines have the same slope but different y-intercepts.

37. Yes; you can find the slope of the line, then substitute the y-intercept for b, and write the equation.

38. y 5 ^}³₂ x 2 ¹^}₂

Answers for the lesson “Use Linear Equations in Slope-Intercept Form”

LESSON

4.2

(4)

39. y 5 ⁹^}₂ x 2 ^}¹₂

40. y 5 ³^}₂ x 1 ^}¹¹₂

41. The lines y 5 ^}³₂ x 2 ¹^}₂ and y 5 ⁹^}₂ x 2 ^}¹₂ and the lines y 5 ⁹^}₂ x 2 ^}¹₂ and y 5 ^}³₂ x 1 ^}¹¹₂ intersect because they have different slopes; the lines

y 5 ³^}₂ x 2 ^}¹₂ and y 5 ^}³₂ x 1 ^}¹¹₂ will not intersect, they have the same

slope, so they are parallel.

42. The three points lie on the same line. If you find the equation of the line between two of the points and then check to see that the third point is a solution, you can see that all three points are on the line y 5 ^}³₄ x 1 1.

43. The three points do not lie on the same line. If you find the equation of the line between two of the points and then check to see that the third point is a solution, you can see they do not lie on the same line.

46. 7; find the equation of the line through (22, 3) and (2, 5) to be y 5 ^}¹₂ x 1 4, then substitute 6 for x to find k.

Problem Solving 47. ^}³₄ ft/yr; 6 ft

48. a. $2.95 b. $25.95

49. 115 min or 1 h 55 min;

substitute 30 for m, 2 for x, and 85 for y into the equation y 5 mx 1 b to find b 5 25. Then substitute 3 for x into the equation y 5 30x 1 25 to solve for y.

(5)

50. a. $358

b. y 5 27.8t 1 358

c. $886.20

51. a. about 584 newspapers

b. y 5 11.8x 1 584

c. about 938 newspapers

52. a. 17,381 airports

b. y 5 175x 1 17,381

c. 2000

53. a. d 5 281t 1 234

b.

2

0 4 6 8 10 12 14

250 225 200 175 150 125 100 75 50 25

0 !

"

d 5 218t 1 234

The slope is the rate that the hurricane is traveling, the y-intercept represents the distance from the town at 12 ^P.^M.

c. 1 ^A.^M.; find the t-intercept to find the value of t when the distance to the town is 0;

substitute 0 for d and solve for t; t 5 13, so you need to add 13 hours to 12 ^P.^M. to get 1 ^A.^M.

54. a. d 5 10t 1 60

b. The rate of change, 10 meters per second, represents the skater’s top racing speed; the initial value, 60, represents the distance the skater traveled from a stand-still to where he reached his top racing speed; d meters 5

1

¹⁰^}seconds^meters

2

(x seconds) 1 60 meters.

c. 54 sec; the total distance is the length of the race track times 3 laps, 600 meters. If you substitute 600 for d, t 5 54.

(6)

Mixed Review

55. 3 ^56. 218

57. 23 ^58. 28.8

59. y 5 25x 2 2

60. y 5 ²^}₇ x 2 3

61. y 5 x 2 4

62. y 5 9x 1 14

63. y 5 2 ^}⁴₅ x 1 6

64. y 5 2 ^}₁₂¹ x 1 2

(7)

Skill Practice 1. 22; (25, 5)

2. Find the slope and substitute it for m in the equation y 2 y₁ 5 m(x 2 x₁). Then pick one of the points and substitute the coordinates in for y₁ and x₁.

3. y 2 1 5 2(x 2 2)

4. y 2 5 5 2(x 2 3)

5. y 1 1 5 26(x 2 7)

6. y 1 1 5 22(x 2 5)

7. y 2 2 5 5(x 1 8)

8. y 2 6 5 ^}³₂ (x 1 6)

9. y 1 3 5 29(x 1 11)

10. y 1 9 5 ^}⁷₃ (x 1 3)

11. y 1 12 5 2 ^}²₅ (x 2 5)

12. C

13. The form y 2 y₁, so the left side should be y 2 (25) or y 1 5;

y 1 5 5 22(x 2 1).

14.

!

"

y 5 3(x 1)

"

15.

"

!

"

y 3 2(x 2)

16.

!

"

y 1 3(x 6)

Answers for the lesson “Write Linear Equations in Point-Slope Form”

LESSON

4.3

(8)

17.

y 8 (x 4)

!

"

!

18.

"

!

"

2"

y 2 1 5 (x 1 1)³₄ 19.

"

!

"

y 4 (x 3)⁵₂

"

20. y 2 1 5 2(x 2 3) or y 1 3 5 2(x 2 1)

21. y 2 4 5 (x 2 1) or y 2 1 5 (x 1 2)

22. y 2 4 5 2 ^}¹₂ (x 1 5) or y 2 2 5 2 ^}¹₂ (x 1 1)

23. y 2 2 5 22(x 2 7) or y 2 12 5 22(x 2 2)

24. y 1 2 5 ¹^}₂ (x 2 6) or y 2 1 5 ¹^}₂ (x 2 12)

25. y 1 1 5 2 ^}³₅ (x 1 4) or y 1 7 5 2 ^}³₅ (x 2 6)

26. y 2 5 5 ⁵^}₄ (x 2 4) or y 1 5 5 ⁵^}₄ (x 1 4)

27. y 1 20 5 8(x 1 3) or y 2 36 5 8(x 2 4)

28. y 1 19 5 ^}¹⁶₅ (x 1 5) or y 2 13 5 ^}¹⁶₅ (x 2 5)

29. A point was not substituted into the equation, the y-coordinates of the two points were substituted;

y 2 2 5 ²^}₃ (x 2 1).

30. B

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31. No; because the increase is not at a constant rate, the situation cannot be modeled by a linear equation.

32. Yes; because the rate is increas- ing at a constant rate, the situation can be modeled by a linear equa- tion. Sample answer:

y 2 1.2 5 ^}¹₅ (x 2 1)

33. No; because the increase is not at a constant rate, the situation cannot be modeled by a linear equation.

34. Yes; because the rate is decreasing at a constant rate, the situation can be modeled by a linear equa- tion. Sample answer:

y 2 16 5 3(x 1 3)

35. 2; y 2 8 5 2(x 2 2) or y 2 6 5 2(x 2 4)

36. 23; y 2 3 5 3(x 2 4) or y 5 3(x 2 3)

Problem Solving 37. a. y 5 130x 1 530

b. $1570

38. Since the cost increases at a constant rate of $1714 per month, the situation can be modeled by a linear equation; $5950; $1714.

39. y 5 10,000x 1 67,000; $127,000

40. a. y 5 1.4x 1 30

b. 45.4 gal

41. a. Since the cost increases at a constant rate of $.49 per print, the situation can be modeled by a linear equation.

b. Sample answer:

y 2 1.98 5 0.49(x 2 1)

c. $1.49 ^d. $1.79

42. a. y 5 2.45x 1 13.45

b. about 26.64 million metric tons

43. a. y 2 17.6 5 20.06(x 2 60)

b. 16.4 ft/sec

44. a. y 5 0.417391x 1 21.413

b. 1.59 billion lb; find the number of cans recycled per pound of aluminum in 2002 by substituting 30 for x to get about 33.9 cans per pound.

Divide 53.8 billion aluminum cans by 33.9 cans per pound to find the number of pounds of aluminum.

(10)

Skill Practice 1. standard form

2. slope-intercept form

3. point-slope form

4. Find the slope of the line then substitute the slope and one of the points into the point-slope form.

Collect variables on one side and constants on the other side.

5–10. Sample answers are given.

5. 2x 1 2y 5 220, 3x 1 3y 5 230

6. x 1 2y 5 3, 10x 1 20y 5 30

7. x 2 2y 5 29, 22x 1 4y 5 18

8. 23x 2 4y 5 2, 26x 2 8y 5 4

9. 3x 2 y 5 24, 6x 2 2y 5 28

10. 2x 2 4y 5 5, 24x 1 8y 5 210

11. 2x 1 y 5 5

12. 23x 1 y 5 213

13. 2x 1 y 5 5

14. 4x 1 y 5 232

15. ³^}₂ x 1 y 5 210

16. 2 ^}¹₆ x 1 y 5 29

17. ²^}₃ x 1 y 5 2 ⁴^}₃

18. 2x 1 y 5 7

19. 2 ^}⁴₃ x 1 y 5 21

20. 24x 1 y 5 23

21. 2 ^}¹₂ x 1 y 5 1

22. y 5 22

23. y 5 2, x 5 3

24. y 5 23, x 5 25

25. y 5 3, x 5 21

26. y 5 3, x 5 5

27. y 5 4, x 5 21

28. y 5 22, x 5 26

29. (1, 24) was substituted incorrectly, 1 should be substituted for x and 24 substituted for y.

A(1) 2 3(24) 5 5, A 1 12 5 5, A 5 27.

30. } 6^x 1 } ^y4 5 1; Sample answer:

I solved the equations 2x 1 3(0) 5 12 and 2(0) 1 3y 5 12 to find a, the x-intercept, and b, the y- intercept, respectively. Then I substituted the values of a and b into the general intercept form.

31. 4; 4x 1 3y 5 5

32. ¹^}₂ ; ^}¹₂ x 2 4y 5 21

33. 24; 2x 2 4y 5 10

Answers for the lesson “Write Linear Equations in Standard Form”

LESSON

4.4

(11)

34. 11; 8x 1 11y 5 4

35. 25; 25x 2 3y 5 25

36. ^}²₇ ; 2x 1 ²^}₇ y 5 24

37. ^}^a_b x 1 y 5 a

Problem Solving

38. 2.5p 1 1.2v 5 300;

Sample answer: 120 phlox plants and 0 vinca plants; 0 phlox plants and 250 vinca plants; 60 phlox plants and 125 vinca plants

39. a. 15 oz

b. 12c 1 15w 5 120

c. 10 corn, 0 wheat; 5 corn, 4 wheat; 0 corn, 8 wheat

40. 20n 1 5t 5 100;

2

0 4 6 8 10 12 14 16 18 20 6

5 4 3 2 1

0 !

"

The n-intercept, 5, is the number of nights of boarding the dog at the kennel without any treats. The t-intercept, 20, is the number of treats that can be bought without boarding the dog for any nights.

41. a. 100* 1 40s 5 1600

b.

2

0 4 6 8 10 12 14 16 40

35 30 25 20 15 10 5

0 #

$

c. Large

rafts Small rafts

16 0

14 5

12 10

10 15

8 20

6 25

4 30

2 35

0 40

42. a. 0.75b 1 s 5 63

b. 18 subway rides; if you ride the bus 60 times, it costs

(0.75)($60) 5 $45 without the pass. The pass costs $63, you need to spend $18 on subway rides, $18 4 $1 5 18.

(12)

43. 2* 1 2w 5 60; Sample answer:

Length (ft) Width (ft)

5 25

10 20

15 15

20 10

25 5

44. a. 0.4x 1 0.6y 5 1000

b. 1200 mL c. 420 mL

Mixed Review of Problem Solving

1. a. $13 per month; $100

b. C 5 13m 1 100

c. $256

2. a. d 5 3.5t 1 5

b. 19 mi

3. a. Because the cost increases at a constant rate of $16 per person, the situation can be modeled by a linear equation.

b. C 5 16p c. $1920

4. V 5 3t; substitute 150 for V and solve for t; t 5 50 minutes.

5. a. Because the same length of path is paved each day, the situation can be modeled by a linear equation.

b. d 5 2 ¹^}₂ t 1 10

c. 20 days

6. Sample answer: 0.05n 1 0.1d 5 3 Nickels Dimes

60 0

50 5

40 10

30 15

20 20

10 25

0 30

7. $190;

0 9 1

(13)

8. $69.50;

5 . 9 6

(14)

Skill Practice 1. perpendicular

2. Identify the slopes of the lines.

If the slopes are negative reciprocals, then the lines are perpendicular.

3. y 5 2x 1 5 4. y 5 2 ^}⁵₂ x 1 23

5. y 5 2 ^}³₅ x 1 2

6. y 5 5x 1 7 7. y 5 6x 1 1

8. y 5 ¹^}₃ x 2 4 ^9. y 5 2x 1 9

10. y 5 x 2 5 11. y 5 3x 1 30

12. parallel: none;

perpendicular: a and b

13. parallel: a and b;

perpendicular: none

14. parallel: none;

perpendicular: none

15. parallel: none;

perpendicular: a and b

16. D

17. The line through points (6, 4) and (4, 1) is perpendicular to the line through points (1, 3) and

(4, 1); the slope of the line through the points (6, 4) and (4, 1) is ^}³₂ , the slope of the line through the points (1, 3) and (4, 1) is 2 ^}²₃ . The slopes are negative reciprocals, so the lines are perpendicular.

18. y 5 2x 19. y 5 2 ^}¹₃ x 2 1

20. y 5 2 ^}¹₅ x 1 2

21. y 5 22x 1 24

22. y 5 ^}⁷₂ x 1 3

23. y 5 2 ^}³₄ x 2 4

24. y 5 2 ^}²₃ x 1 5

25. y 5 2 ^}¹₂ x 2 ^}¹₂

26. y 5 2x 2 17

27. (2, 1) was substituted incorrectly, 2 should be substituted for x, and 1 should be substituted for y;

1 5 2(2) 1 b, 1 5 4 1 b, 23 5 b.

28. B

Answers for the lesson “Write Equations of Parallel and Perpendicular Lines”

LESSON

4.5

(15)

29. Yes; the slope of the line through (4, 3) and (3, 21) is 4 and the slope of the line through (23, 3) and (1, 2) is 2 ^}¹₄ . The slopes are negative reciprocals, so the lines are perpendicular.

30. Sample answer: y 5 2x 1 1 and y 5 2x 1 3; y 5 2 ¹^}₂ x 1 2

31. m 5 ^x^}_y¹^{2 x}²

1 2 y₂

Problem Solving 32. a. y 5 2x 1 8

b. y 5 22x 1 8

c. No; the slopes 22 and 2 are not negative reciprocals.

33. a. w₁ 5 200d 1 6000;

w₂ 5 200d 1 6250

b. 12,000 lb; 12,250 lb

c. The graphs of the lines are parallel because they have the same slope, 200.

The w-intercept of the second line is 250 more than the w-intercept of the first line.

34. Parallel: 2nd Street and Park Street; the slope of both streets is ²^}₃ . Since they have the same slope, the streets are parallel.

Perpendicular: 2nd Street and Sea Street, Park Street and Sea Street;

the slope of Sea Street is 2 ^}³₂ , which is the negative reciprocal of ^}²₃ , the slope of 2nd Street and Park Street. Since the slopes are negative reciprocals, the streets are perpendicular.

35. Different registration fees;

because the lines are parallel, the rate of change, the monthly fee, for each must be equal. Therefore, the students paid different

registration fees.

36. a. C 5 38.75m 1 49

b. C 5 38.75m 1 149

c. The graphs of the lines are parallel; they have the same slope, 38.75. The C-intercept of the second graph is 100 more than the C-intercept of the first graph.

d. $100; $100

(16)

37. a. y 5 22.5x 1 50;

y 5 22.5x 1 30

b. The graphs of the lines are parallel; they have the same slope, 22.5. The y-intercept of the second line is 20 less then the y-intercept of the first line.

c. 20; 12; the x-intercepts show the number of months of nonuse it would take for the value of the gift card to be $0.

(17)

Skill Practice 1. increase

2. When data have a positive correlation, the dependent variable tends to increase as the independent variable increases.

When data have a negative correlation, the dependent variable tends to decrease as the independent variable increases.

When data have relatively no correlation where there is no apparent relationship between the independent variable and the dependent variable.

3. positive correlation

4. relatively no correlation

5. negative correlation

6. Sample answer: y 5 11.5x 2 0.28

0 1 2 3 4 5 6 7 8 9 !

"

0 10 20 30 40 50 60 70 80 90 100

7. Sample answer:

y 5 24.5x 1 15.4

!

2" !

"

8. C

9. The line does not have approximately half the data above it and half below it.

2!

"

!

"

10. The independent variable is x, not y; the dependent variable decreases as x increases.

11. Sample answer: The amount of time driving a car and the amount of gas left in the gas tank.

Answers for the lesson “Fit a Line to Data”

LESSON

4.6

(18)

12.

!#

!

"

2$

relatively no correlation; no;

because there is relatively no correlation in the data you cannot write an equation.

13.

20 30

10 40 50 60 70 80 90 100 !

"

0 30 15 60 75 45 90 105 120 135

positive correlation;

Sample answer: y 5 1.49x 2 13

14.

!

"

2$

relatively no correlation

15. Line b; line a has too many points below the line, but line b has about half the points above the line and about half the points below the line.

Problem Solving 16. a.

0 40 80 120 160 !

"

0 8 16 24 32 40 48

b. Positive correlation; the larger the home range size the larger the percent of pacing time.

c. No; it is below the expected percent of time spent pacing.

(19)

17. a. " ₁₀_{20 30}40 50 60 70 80 90 !

290 2100 270 260 280 250 240 230 220 210 0

b. Sample answer:

y 5 22.2x 1 111

c. Sample answer:

22.2 degrees per kilometer

18.

0 9 18 27 36 45 54 !

"

0 2 4 6 8 10 12 14 16 18 20

0 9 18 27 36 45 54 !

"

0 4 6 8 10 12 14 16 18 20 22 24

The growth rate of alligator 2 is slightly greater than the growth rate of alligator 1.

19. Sample answer: y 5 12.6x 1 32

20. a. Sample answer: y 5 1.2x 1 30

b. Sample answer:

1.2 min per day

c. No; it will continue through June and then start decreasing.

21. a. Sample answer:

h 5 17.8y 1 93.6

b. Sample answer:

m 5 0.78h 2 33.2

c. Sample answer:

m 5 13.884y 1 39.808; the function models the amount of money, m, spent on the Internet as a function of the number of years, y, since 1999.

(20)

21. d. Yes; if you substitute the number of years since 1999 for y, you get about the amount of money, m, given in the data.

(21)

Skill Practice

1. linear interpolation

2. Extrapolation is finding an approximate value ouside the range of known values.

Interpolation is finding an approximate value within the range of known values.

3. y 5 2.6x 1 2.3; 15.3

2 3 1

0 4 5 6 7 !

"

0 4 2 8 10 6 12 14 16 18 20

4. y 5 8.2x 2 10.1; 30.9

0 2 4 6 8 10 !

"

0 10 20 30 40 50 60 70

5. y 5 10.7x 1 20; 127

2 3 1

0 4 5 6 !

"

0 20 10 40 50 30 60 70

6. y 5 0.33x 1 0.22; 3.52

0 1 2 3 4 5 6 7 8 9 !

"

0 0.5 1 1.5 2 2.5 3

7. 2 ^}²₃ ^8. 7 ^9. 216

10. 4 11. 1.5 12. 1.4

13. To find the zero of a function, substitute 0 for y, not x;

0 5 2.3x 2 2, 2 5 2.3x, x 5 ^}²⁰₂₃ .

14. B

15. a and b were not substituted correctly; y 5 4.47x 1 23.1.

Answers for the lesson “Predict with Linear Models”

LESSON

4.7

(22)

16. Sample answer: Temperature on a mountain depends on the elevation.

The zero indicates the elevation at which the temperature is 08F.

17. a. No; the data would first have a posititve slope and then a negative slope.

b. You could fit a line to the data for the first 10 years and then fit another line to the data for the following 10 years.

Problem Solving 18. a.

0 10 12 14 16 18 20 22 24 !

"

0 1000 2000 3000 4000 5000 6000 7000

b. y 5 513x 2 5258

c. $5002

19. a.

"

2 1 4 5 3 6 7 8

b. y 5 0.03x 1 1.23

c. about 8.73 ft²

20. a. y 5 31.5x 1 1540

b. 2004

21. a. y 5 2197.6x 1 3542

b. about 17.9; 17.9 years from 1985 the number of people living in high noise areas will be 0; no.

22. a. Sample answer:

!

"

!

" #$ %&

&

"

!

#$

%"

#%

b. Answers may vary; best fitting line: y 5 20.2x 1 19.7;

answers may vary.

(23)

22. c. The slope, 20.2, is the change in the cost (in thousands of dollars per thousand miles) of a local car of the same model, make, and year, and the

y-intercept, 19.7, is the predi- cated selling price (in thousands of dollars) for a local car of the same model, make, and year with a mileage of 0.

23. a.

0 5 10 15 20 25 !

"

0 2000 4000 6000 8000

0 5 10 15 20 25 !

"

0 10,000 20,000 30,000 40,000

There is relatively no correlation in either scatter plot.

b. No; because you cannot find a line of best fit for either correlation, you cannot use the mallard duck population

to predict the total duck population.

Mixed Review of Problem Solving

1. a.

0 1 2 3 4 5 !

"

0 1200 1600 2000 2400 2800

Years since 1995

Value (millions of dollars)

b. y 5 321x 1 1260

c. about $321 million per year

d. 2002

2. 2;

2

(24)

3. Sample answer: y 5 8x 1 5

4.

0 15 16 17 !

"

0 69 71 73 75

positive correlation

5. a. y 5 21.1x 1 9.1

b. about 21.1 percent per year

c. 8.3; 8.3 years after 1998,

or 2006, the percent of revenue from U.S. music sales made through music clubs will be 0.

6. C 5 4g 1 2.25, C 5 4g 1 1.75;

the graphs have the same slopes, but different C-intercepts.