# Exercises: Find the Equation of a Line (3.11)

## Exercises: Find an Equation of the Line Given the Slope and ${\color{White}{y}}$-Intercept

Instructions: For questions 1-16, 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 $(0,5)$

2. slope $4$ and $y$-intercept $(0,1)$
Solution

$y=4x+1$

3. slope $6$ and $y$-intercept $(0,-4)$

4. slope $8$ and $y$-intercept $(0,-6)$
Solution

$y=8x-6$

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

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

$y=-x+7$

7. slope $-2$ and $y$-intercept $(0,-3)$

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

$y=-3x-1$

9. slope $\frac{3}{5}$ and $y$-intercept $(0,-1)$

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

$y=\frac{1}{5}x-5$

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

12. slope $-\frac{2}{3}$ and $y$-intercept $(0,-3)$
Solution

$y=-\frac{2}{3}x-3$

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

14. slope $0$ and $y$-intercept $(0,2)$
Solution

$y=2$

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

16. slope $-4$ and $y$-intercept $(0,0)$
Solution

$y=-4x$

## Exercises: Find the Equation of a Line Shown on a Graph

Instructions: For questions 17-24, find the equation of the line shown in each graph. Write the equation in slope–intercept form.

17.

18.

Solution

$y=-2x+4$

19.

20.

Solution

$y=\frac{3}{4}x+2$

21.

22.

Solution

$y=-\frac{3}{2}x-1$

23.

24.

Solution

$y=6$

## Exercises: Find an Equation of the Line Given the Slope and a Point

Instructions: For questions 25-42, find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

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

26. $m=\frac{3}{8}$, point $(8,2)$
Solution

$y=\frac{3}{8}x-1$

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

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

$y=\frac{5}{6}x+2$

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

30. $m=-\frac{3}{5}$, point $(10,-5)$
Solution

$y=-\frac{3}{5}x+1$

31. $m=-\frac{1}{4}$, point $(-12,-6)$

32. $m=-\frac{1}{3}$, point $(-9,-8)$
Solution

$y=-\frac{1}{3}x-11$

33. Horizontal line containing $(-2,5)$

34. Horizontal line containing $(-1,4)$
Solution

$y=4$

35. Horizontal line containing $\left(-2,-3\right)$

36. Horizontal line containing $(-1,-7)$
Solution

$y=-7$

37. $m=-\frac{3}{2}$, point $(-4,-3)$

38. $m=-\frac{5}{2}$, point $(-8,-2)$
Solution

$y=-\frac{5}{2}x-22$

39. $m=-7$, point $(-1,-3)$

40. $m=-4$, point $(-2,-3)$
Solution

$y=-4x-11$

41. Horizontal line containing $(2,-3)$

42. Horizontal line containing $(4,-8)$
Solution

$y=-8$

## Exercises: Find an Equation of the Line Given Two Points

Instructions: For questions 43-68, find the equation of a line containing the given points. Write the equation in slope–intercept form.

43. $\left(2,6\right)$ and $\left(5,3\right)$

44. $\left(3,1\right)$ and $\left(2,5\right)$
Solution

$y=-4x+13$

45. $\left(4,3\right)$ and $\left(8,1\right)$

46. $\left(2,7\right)$ and $\left(3,8\right)$
Solution

$y=x+5$

47. $\left(-3,-4\right)$ and $\left(5-2\right)$

48. $\left(-5,-3\right)$ and $\left(4,-6\right)$
Solution

$y=-\frac{1}{3}x-\frac{14}{3}$

49. $\left(-1,3\right)$ and $\left(-6,-7\right)$

50. $\left(-2,8\right)$ and $\left(-4,-6\right)$
Solution

$y=7x+22$

51. $\left(6,-4\right)$ and $\left(-2,5\right)$

52. $\left(3,-2\right)$ and $\left(-4,4\right)$
Solution

$y=-\frac{6}{7}x+\frac{4}{7}$

53. $\left(0,4\right)$ and $\left(2,-3\right)$

54. $\left(0,-2\right)$ and $\left(-5,-3\right)$
Solution

$y=\frac{1}{5}x-2$

55. $\left(7,2\right)$ and $\left(7,-2\right)$

56. $\left(4,2\right)$ and $\left(4,-3\right)$
Solution

$x=4$

57. $\left(-7,-1\right)$ and $\left(-7,-4\right)$

58. $\left(-2,1\right)$ and $\left(-2,-4\right)$
Solution

$x=-2$

59. $\left(6,1\right)$ and $\left(0,1\right)$

60. $\left(6,2\right)$ and $\left(-3,2\right)$
Solution

$y=2$

61. $\left(3,-4\right)$ and $\left(5,-4\right)$

62. $\left(-6,-3\right)$ and $\left(-1,-3\right)$
Solution

$y=-3$

63. $\left(4,3\right)$ and $\left(8,0\right)$

64. $\left(0,0\right)$ and $\left(1,4\right)$
Solution

$y=4x$

65. $\left(-2,-3\right)$ and $\left(-5,-6\right)$

66. $\left(-3,0\right)$ and $\left(-7,-2\right)$
Solution

$y=\frac{1}{2}x+\frac{3}{2}$

67. $\left(8,-1\right)$ and $\left(8,-5\right)$

68. $\left(3,5\right)$ and $\left(-7,5\right)$
Solution

$y=5$

## Exercises: Find an Equation of a Line Parallel to a Given Line

Instructions: For questions 69-84, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

69. line $y=4x+2$, point $\left(1,2\right)$

70. line $y=3x+4$, point $\left(2,5\right)$
Solution

$y=3x-1$

71. line $y=-2x-3$, point $\left(-1,3\right)$

72. line $y=-3x-1$, point $\left(2,-3\right)$
Solution

$y=-3x+3$

73. line $3x-y=4$, point $\left(3,1\right)$

74. line $2x-y=6$, point $\left(3,0\right)$
Solution

$y=2x-6$

75. line $4x+3y=6$, point $\left(0,-3\right)$

76. line $2x+3y=6$, point $\left(0,5\right)$
Solution

$y=-\frac{2}{3}x+5$

77. line $x=-3$, point $\left(-2,-1\right)$

78. line $x=-4$, point $\left(-3,-5\right)$
Solution

$x=-3$

79. line $x-2=0$, point $\left(1,-2\right)$

80. line $x-6=0$, point $\left(4,-3\right)$
Solution

$x=4$

81. line $y=5$, point $\left(2,-2\right)$

82. line $y=1$, point $\left(3,-4\right)$
Solution

$y=-4$

83. line $y+2=0$, point $\left(3,-3\right)$

84. line $y+7=0$, point $\left(1,-1\right)$
Solution

$y=-1$

## Exercises: Find an Equation of a Line Perpendicular to a Given Line

Instructions: For questions 85-96, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

85. line $y=-2x+3$, point $\left(2,2\right)$

86. line $y=-x+5$, point $\left(3,3\right)$
Solution

$y=x$

87. line $y=\frac{3}{4}x-2$, point $\left(-3,4\right)$

88. line $y=\frac{2}{3}x-4$, point $\left(2,-4\right)$
Solution

$y=-\frac{3}{2}x-1$

89. line $2x-3y=8$, point $\left(4,-1\right)$

90. line $4x-3y=5$, point $\left(-3,2\right)$
Solution

$y=-\frac{3}{4}x-\frac{1}{4}$

91. line $2x+5y=6$, point $\left(0,0\right)$

92. line $4x+5y=-3$, point $\left(0,0\right)$
Solution

$y=\frac{5}{4}x$

93. line $y-3=0$, point $\left(-2,-4\right)$

94. line $y-6=0$, point $\left(-5,-3\right)$
Solution

$x=-5$

95. line $y$-axis, point $\left(3,4\right)$

96. line $y$-axis, point $\left(2,1\right)$
Solution

$y=1$

## Exercises: Mixed Practice

Instructions: For questions 97-114, find the equation of each line. Write the equation in slope–intercept form.

97. Containing the points $\left(4,3\right)$ and $\left(8,1\right)$

98. Containing the points $\left(2,7\right)$ and $\left(3,8\right)$
Solution

$y=x+5$

99. $m=\frac{1}{6}$, containing point $\left(6,1\right)$

100. $m=\frac{5}{6}$, containing point $\left(6,7\right)$
Solution

$y=\frac{5}{6}x+2$

101. Parallel to the line $4x+3y=6$, containing point $\left(0,-3\right)$

102. Parallel to the line $2x+3y=6$, containing point $\left(0,5\right)$
Solution

$y=-\frac{2}{3}x+5$

103. $m=-\frac{3}{4}$, containing point $\left(8,-5\right)$

104. $m=-\frac{3}{5}$, containing point $\left(10,-5\right)$
Solution

$y=-\frac{3}{5}x+1$

105. Perpendicular to the line $y-1=0$, point $\left(-2,6\right)$

106. Perpendicular to the line $y$-axis, point $\left(-6,2\right)$
Solution

$y=2$

107. Containing the points $\left(4,3\right)$ and $\left(8,1\right)$

108. Containing the points $\left(-2,0\right)$ and $\left(-3,-2\right)$
Solution

$y=x+2$

109. Parallel to the line $x=-3$, containing point $\left(-2,-1\right)$

110. Parallel to the line $x=-4$, containing point $\left(-3,-5\right)$
Solution

$x=-3$

111. Containing the points $\left(-3,-4\right)$ and $\left(2,-5\right)$

112. Containing the points $\left(-5,-3\right)$ and $\left(4,-6\right)$
Solution

$y=-\frac{1}{3}x-\frac{14}{3}$

113. Perpendicular to the line $x-2y=5$, containing point $\left(-2,2\right)$

114. Perpendicular to the line $4x+3y=1$, containing point $\left(0,0\right)$
Solution

$y=\frac{3}{4}x$

## Exercises: Everyday Math

Instructions: For questions 115-116, answer the given everyday math word problems.
115. Cholesterol. The age, $x$, and LDL cholesterol level, $y$, of two men are given by the points $\left(18,68\right)$ and $\left(27,122\right)$. Find a linear equation that models the relationship between age and LDL cholesterol level.

116. Fuel consumption. The city mpg, $x$, and highway mpg, $y$, of two cars are given by the points $\left(29,40\right)$ and$\left(19,28\right)$. Find a linear equation that models the relationship between city mpg and highway mpg.
Solution

$y=1.2x+5.2$

## Exercises: Writing Exercises

Instructions: For questions 117-118, answer the given writing exercises.
117. Why are all horizontal lines parallel?

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