Extra Practice - Mrs. Rohlwing

[Pages:4]Name

Class

Date

Extra Practice

Chapter 5

Lesson 5-1

Find the slope of each line.

1.

y

2

x -2 O 2

-2

2.

y

2

x -2 O 2

-2

3.

y

2

x -2 O 2

-2

2

1

Find the rate of change for each situation. 3

undefined

4. growing from 1.4 m to 1.6 m in one year 0.2 m/yr

5. bicycling 3 mi in 15 min and 7 mi in 55 min 0.1 mi/min

6. growing 22.4 mm in 14 s 1.6 mm/s

7. reading 8 pages in 9 min and 22 pages in 30 min

2 3

page

per

minute

8. e cost of four movie tickets is $30 and the cost of seven tickets is $52.50. $7.50/ticket

9. Five seconds after jumping out of the plane, a sky diver is 10,000 ft above the ground. After 30 seconds, the sky diver is 3750 ft above the ground. 250 ft/s

10. Find the slope of the line that includes the points (1, 4) and (3, 2).

3 2

Lesson 5-2

Tell whether each equation is a direct variation. If it is, nd the constant of variation.

11. y 2x 2 no

12. 4y x

yes;

1 4

13.

y x

3

yes; 3

Graph the direct variation that includes the given point. Write the equation of the line.

14. (5, 4) 4y

y

4 5

x

2

O

x

24

15. (7, 7) y x

6y 5 4 3 2

16.

(3,

10)

y

10 3

x

17.

(4, 8)

y 2x

yO

y

-4 -2

x

4

-2

x

-4

-6

O 246

O

x

12 34 5 6

-6

-8

-10

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Name

Class

Date

Extra Practice (continued)

Chapter 5

Write a direct variation to model each situation. en answer the question.

18. After 30 minutes, a car moving at a constant speed has traveled 25 miles. Moving at the

same speed, how far will it travel in 140 minutes?

50t about

d in hours; 117 mi

56t

d

in

minutes

19. What is the perimeter of a square with side length 13.4 inches? P 4s; 53.6 in.

Lesson 5-3

Find the slope and y-intercept.

20. y 6x 8

slope 6, y-intercept 8

23.

y

3 4

x

8

slope 34, y-intercept 8

21. 3x 4y 24 slope 34, y-intercept 6

24. 2y 3x 1

slope

3 2

,

y-intercept

12

22. 2y 8

slope 0, y-intercept 4

25. 4x 5y 2

slope

4 5

,

y-intercept

25

A line passes through the given points. Write an equation for the line in slope-intercept form.

26. (2, 4) and (3, 9) yx6

29. (7, 0) and (3, 4) yx7

27. (1, 6) and (9, 4) y 54x 714

30. (0, 0) and (7, 1) y 17 x

28. (0, 7) and (1, 0) y 7x 7

31. (10, 0) and (0, 7) y 170 x 7

Graph each equation.

2y

32. y 2x 3

-2 O 2

-2

x

33.

y

2 3

x

4

4

y

O

24

x

-2

Write an equation in slope-intercept form for each situation.

34. A skateboard ramp is 5 ft high and 12 ft long from end to end.

y

5 12

x

35. An airplane with no fuel weighs 2575 lbs. Each gallon of gasoline added to

the fuel tanks weighs 6 lbs. y 6x 2575

Lessons 5-4 and 5-5

Write an equation in point-slope form for the line through the given point with the given slope.

36. (4, 6); m 5 y 6 5(x 4)

37. (3, 1); m 1 y1x3

38.

(8,

5);

m

1 2

y

5

1 2

(

x

8)

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Name

Extra Practice (continued)

Chapter 5

Class

Date

Find the x- and y-intercepts for each equation.

39. y 7x

x-intercept 0, y-intercept 0 Graph each equation.

40.

y

1 2

x

3

x-intercept 6,

y-intercept 3

41. 2y 5x 12

x-intercept

12 5

,

y-intercept 6

42. x 4y 8 4y x O 48

45. 4x 3y 12 y x

O 24 -2

-4

43. y 5 2(x 1) y

3

-2

O -1

46. y 1 2y

-2 O -2

x 3

x 2

44. x 3 0 2y x

-2 O 2 -2

47. y 1 12(x 2) y x

-2 O 2

-4

Write an equation in point-slope form for each situation.

48. A train travels at a rate of 70 mi/h. Two hours after leaving the station it

is 210 miles from its destination. y 210 70(x 2)

49.

An escalator has a 24 feet above the

slope oor.

of y

34. A2f4ter tr34a(xvelin3g2f)orward

32

feet,

the

escalator

is

Write an equation in standard form for each situation.

50. Juan can ride his bike at 12 mi/h and walk at 4 mi/h. Write an equation that relates the amount of time he can spend riding or walking combined, to travel 20 miles. 12b 4w 20

51. You have $25 to buy supplies for a class party. Juice costs $3 per bottle and chips cost $2 per bag. Write an equation that relates the amount of juice and chips you can buy using $25. 3j 2c 25

Lesson 5-6

Write an equation in standard form that satis es the given conditions.

52. parallel to y 4x 1, through (3, 5) 4x y 17

53. perpendicular to y x 3, through (0, 0) x y 0

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Name

Class

Date

Extra Practice (continued)

Chapter 5

54. perpendicular to 3x 4y 12, through (7, 1) 4x 3y 25

55. parallel to 2x y 6, through (6, 9) 2x y 3

56. parallel to the x-axis and through (4, 1) 57. through (4, 44) and parallel to the y-axis

y 1

x4

Tell whether each statement is true or false. Explain your choice.

58. Two airplanes traveling at the same rate leave an airport 1 hour apart. e graphs of the distance each plane travels will be parallel. True; the same rate of travel means that slopes of the graphs are the same, so the lines are parallel.

59. Two lines with negative slopes can be perpendicular. False; the slopes of perpendicular lines have a product of 1, so one must be positive and the other must be negative.

Lesson 5-7 12

60. a. Graph the (ages, grades) data of some students in a school.

11

(10, 6), (16, 10), (15, 10), (18, 12), (17, 11),

10

Grade

(17, 12), (19, 12), (16, 11), (11, 7), (15, 9), (13, 8)

9

8

b. Draw a trend line.

7

c. Find the equation of the line of best t.

6

grade 0.720 age 1.118

61. Use a calculator to nd a line of best t for the data in the chart at the right. Find the value of the correlation coe cient r. Let x 0 correspond to 1960. y 0.11x 7.3; 0.8466

0 4 8 12 16 20 Age (yr)

Total U.S. Vehicle Production (millions)

1960 1970 1980 1990 2000

7.9

8.8

8.0

9.8 12.8

Lesson 5-8

Graph each equation by translating y U x U or y U x U .

62. A car traveling at a rate of 50 mi/h passes a rest area 30 minutes after the beginning of the trip. Write an absolute value equation that represents the car's distance from the rest area. y 50U x 0.5 U

63. y U x U 1

64. y U x 2 U

65. y U x 1 U

4y

x -2 O 2

4y

x -4 -2 O

y

x

-4

O2

-2

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