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 $$(0,5)$$

$$y=3x+5$$

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

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

$$y=−3x−1$$

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

5. slope $$\frac{1}{5}$$ and $$y$$-intercept $$(0,−5)$$

$$y=\frac{1}{5}x−5$$

6. slope $$−\frac{3}{4}$$ and $$y$$-intercept $$(0,−2)$$

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

$$y=−1$$

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.

$$y=3x−5$$

10.

11.

$$y=\frac{1}{2}x−3$$

12.

13.

$$y=−\frac{4}{3}x+3$$

14.

15.

$$y=−2$$

16.

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. $$m=\frac{5}{8}$$, point $$(8,3)$$

$$y=\frac{5}{8}x−2$$

18. $$m=\frac{5}{6}$$, point $$(6,7)$$

19. $$m=−\frac{3}{5}$$, point $$(10,−5)$$

$$y=−\frac{3}{5}x+1$$

20. $$m=−\frac{3}{4}$$, point $$(8,−5)$$

21. $$m=−\frac{3}{2}$$, point $$(−4,−3)$$

$$y=−\frac{3}{2}x+9$$

22. $$m=−\frac{5}{2}$$, point $$(−8,−2)$$

23. $$m=−7$$, point $$(−1,−3)$$

$$y=−7x−10$$

24. $$m=−4$$, point $$(−2,−3)$$

25. Horizontal line containing $$(−2,5)$$

$$y=5$$

26. Horizontal line containing $$(−2,−3)$$

27. Horizontal line containing $$(−1,−7)$$

$$y=−7$$

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 $$(5,3)$$

$$y=−x+8$$

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

31. $$(−3,−4)$$ and $$(5−2)$$.

$$y=\frac{1}{4}x−\frac{13}{4}$$

32. $$(−5,−3)$$ and $$(4,−6)$$.

33. $$(−1,3)$$ and $$(−6,−7)$$.

$$y=2x+5$$

34. $$(−2,8)$$ and $$(−4,−6)$$.

35. $$(0,4)$$ and $$(2,−3)$$.

$$y=−\frac{7}{2}x+4$$

36. $$(0,−2)$$ and $$(−5,−3)$$.

37. $$(7,2)$$ and $$(7,−2)$$.

$$x=7$$

38. $$(−2,1)$$ and $$(−2,−4)$$.

39. $$(3,−4)$$ and $$(5,−4)$$.

$$y=−4$$

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 $$(1,2)$$

$$y=4x−2$$

42. line $$y=−3x−1$$, point $$2,−3)$$.

43. line $$2x−y=6$$, point $$(3,0)$$.

$$y=2x−6$$

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

45. line $$x=−4$$, point $$(−3,−5)$$.

$$x=−3$$

46. line $$x−2=0$$, point $$(1,−2)$$

47. line $$y=5$$, point $$(2,−2)$$

$$y=−2$$

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 $$(2,2)$$

$$y=\frac{1}{2}x+1$$

50. line $$y=−x+5$$, point $$(3,3)$$

51. line $$y=\frac{3}{4}x−2$$, point $$(−3,4)$$

$$y=−\frac{4}{3}x$$

52. line $$y=\frac{2}{3}x−4$$, point $$(2,−4)$$

53. line $$2x−3y=8$$, point $$(4,−1)$$

$$y=−\frac{3}{2}x+5$$

54. line $$4x−3y=5$$, point $$(−3,2)$$

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

$$y=\frac{5}{2}x$$

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

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

$$y=4$$

58. line $$x=−5$$, point $$(1,−2)$$

59. line $$x=7$$, point $$(−3,−4)$$

$$y=−4$$

60. line $$x=−1$$, point $$(−4,0)$$

61. line $$y−3=0$$, point $$(−2,−4)$$

$$x=−2$$

62. line $$y−6=0$$, point $$(−5,−3)$$

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

$$y=4$$

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 $$(8,1)$$

$$y=−\frac{1}{2}x+5$$

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

67. $$m=\frac{1}{6}$$, containing point $$(6,1)$$

$$y=\frac{1}{6}x$$

68. $$m=\frac{5}{6}$$, containing point $$(6,7)$$

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

$$y=−\frac{4}{3}x−3$$

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

71. $$m=−\frac{3}{4}$$, containing point $$(8,−5)$$

$$y=−\frac{3}{4}x+1$$

72. $$m=−\frac{3}{5}$$, containing point $$(10,−5)$$

73. Perpendicular to the line $$y−1=0$$, point $$(−2,6)$$

$$x=−2$$

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

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

$$x=−2$$

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

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

$$y=−\frac{1}{5}x−\frac{23}{5}$$

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

79. Perpendicular to the line $$x−2y=5$$, point $$(−2,2)$$

$$y=−2x−2$$

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

Writing Exercises

81. Why are all horizontal lines parallel?