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Mathematics LibreTexts

3.3E: Exercises

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Practice Makes Perfect

Find an Equation of the Line Given the Slope and y-Intercept

In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope-intercept form.

1. slope 3 and y-intercept (0,5)

Answer

y=3x+5

2. slope 8 and y-intercept (0,6)

3. slope 3 and y-intercept (0,1)

Answer

y=3x1

4. slope 1 and y-intercept (0,3)

5. slope 15 and y-intercept (0,5)

Answer

y=15x5

6. slope 34 and y-intercept (0,2)

7. slope 0 and y-intercept (0,1)

Answer

y=1

8. slope 4 and y-intercept (0,0)

In the following exercises, find the equation of the line shown in each graph. Write the equation in slope-intercept form.

9.
This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 5), (1, negative 2), and (2, 1).

Answer

y=3x5

10.
This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 4), (1, 2), and (2, 0).

11.
This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (2, negative 2), and (6, 0).

Answer

y=12x3

12.
This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (4, 5), and (8, 8).

13.
This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 3), (3, negative 1), and (6, negative 5).

Answer

y=43x+3

14.
This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 1), (2, negative 4), and (4, negative 7).

15.
This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (1, negative 2), and (2, negative 2).

Answer

y=2

16.
This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 6), (1, 6), and (2, 6).

Find an Equation of the Line Given the Slope and a Point

In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form.

17. m=58, point (8,3)

Answer

y=58x2

18. m=56, point (6,7)

19. m=35, point (10,5)

Answer

y=35x+1

20. m=34, point (8,5)

21. m=32, point (4,3)

Answer

y=32x+9

22. m=52, point (8,2)

23. m=7, point (1,3)

Answer

y=7x10

24. m=4, point (2,3)

25. Horizontal line containing (2,5)

Answer

y=5

26. Horizontal line containing (2,3)

27. Horizontal line containing (1,7)

Answer

y=7

28. Horizontal line containing (4,8)

Find an Equation of the Line Given Two Points

In the following exercises, find the equation of a line containing the given points. Write the equation in slope-intercept form.

29. (2,6) and (5,3)

Answer

y=x+8

30. (4,3) and (8,1)

31. (3,4) and (52).

Answer

y=14x134

32. (5,3) and (4,6).

33. (1,3) and (6,7).

Answer

y=2x+5

34. (2,8) and (4,6).

35. (0,4) and (2,3).

Answer

y=72x+4

36. (0,2) and (5,3).

37. (7,2) and (7,2).

Answer

x=7

38. (2,1) and (2,4).

39. (3,4) and (5,4).

Answer

y=4

40. (6,3) and (1,3)

Find an Equation of a Line Parallel to a Given Line

In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form.

41. line y=4x+2, point (1,2)

Answer

y=4x2

42. line y=3x1, point 2,3).

43. line 2xy=6, point (3,0).

Answer

y=2x6

44. line 2x+3y=6, point (0,5).

45. line x=4, point (3,5).

Answer

x=3

46. line x2=0, point (1,2)

47. line y=5, point (2,2)

Answer

y=2

48. line y+2=0, point (3,3)

Find an Equation of a Line Perpendicular to a Given Line

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope-intercept form.

49. line y=2x+3, point (2,2)

Answer

y=12x+1

50. line y=x+5, point (3,3)

51. line y=34x2, point (3,4)

Answer

y=43x

52. line y=23x4, point (2,4)

53. line 2x3y=8, point (4,1)

Answer

y=32x+5

54. line 4x3y=5, point (3,2)

55. line 2x+5y=6, point (0,0)

Answer

y=52x

56. line 4x+5y=3, point (0,0)

57. line x=3, point (3,4)

Answer

y=4

58. line x=5, point (1,2)

59. line x=7, point (3,4)

Answer

y=4

60. line x=1, point (4,0)

61. line y3=0, point (2,4)

Answer

x=2

62. line y6=0, point (5,3)

63. line y-axis, point (3,4)

Answer

y=4

64. line y-axis, point (2,1)

Mixed Practice

In the following exercises, find the equation of each line. Write the equation in slope-intercept form.

65. Containing the points (4,3) and (8,1)

Answer

y=12x+5

66. Containing the points (2,0) and (3,2)

67. m=16, containing point (6,1)

Answer

y=16x

68. m=56, containing point (6,7)

69. Parallel to the line 4x+3y=6, containing point (0,3)

Answer

y=43x3

70. Parallel to the line 2x+3y=6, containing point (0,5)

71. m=34, containing point (8,5)

Answer

y=34x+1

72. m=35, containing point (10,5)

73. Perpendicular to the line y1=0, point (2,6)

Answer

x=2

74. Perpendicular to the line y-axis, point (6,2)

75. Parallel to the line x=3, containing point (2,1)

Answer

x=2

76. Parallel to the line x=4, containing point (3,5)

77. Containing the points (3,4) and (2,5)

Answer

y=15x235

78. Containing the points (5,3) and (4,6)

79. Perpendicular to the line x2y=5, point (2,2)

Answer

y=2x2

80. Perpendicular to the line 4x+3y=1, point (0,0)

Writing Exercises

81. Why are all horizontal lines parallel?

Answer

Answers will vary.

82. Explain in your own words why the slopes of two perpendicular lines must have opposite signs.

Self Check

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

The figure shows a table with six rows and four columns. The first row is a header row and it labels each column. The first column header is “I can…”, the second is “confidently”, the third is “with some help”, “no minus I don’t get it!”. Under the first column are the phrases “find the equation of the line given the slope and y-intercept”, “find an equation of the line given the slope and a point”, “find an equation of the line given two points”, “find an equation of a line parallel to a given line”, and “find an equation of a line perpendicular to a given line”. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved.

b. What does this checklist tell you about your mastery of this section? What steps will you take to improve?


This page titled 3.3E: Exercises is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

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