Graphing Linear Equations Chapter Questions

1. What are the various types of information you can be given to graph a line?

2. What is slope? How is it determined?

3. Why do we need to be careful about the slopes of horizontal and vertical lines?

4. How can we tell is two lines are parallel, perpendicular or neither just from their equations?

5. What are the various ways you can use information given to you to determine the equation of a line?

Graphing Linear Equations Chapter Problems

Graph using a table

Classwork

For the equations below, make a table with at least 3 ordered pairs, plot the points and connect them to form the line.

1. y = 3x – 42. y = -2x + 43. y = x – 3

4. y = 12

x + 4

5. y = - 23x + 1

Homework

For the equations below, make a table with at least 3 ordered pairs, plot the points and connect them to form the line.

6. y = -x – 2 7. y = 2x + 1

8. y = 14 x

9. y = -2x – 2

10. y = - 13x + 4

Graph using the slope and y-intercept

Classwork

11. Use lines A, B, C and D to answers the questions.

a. What is the y-intercept of each line?b. Is the slope of each line positive, negative, zero or undefined?

12. What is the slope of lines E, F, G and H?

13. What are the equations of lines E, F ,G and H?

Homework

14. Use lines I, J, K and L to answers the questions.

a. What is the y-intercept of each line?b. Is the slope of each line positive, negative, zero or undefined?

15. What are the slopes of lines M, N, O and P?

16. What is the equation of lines M, N, O and P?

Graph using point slope

Classwork

Graph each equation

17. y – 2 = (x – 3)18. y + 5 = 2(x + 2)19. y – 4 = -3(x – 3)

20. y + 7 = 12 (x – 1)

21. y – 3 = - 34

(x + 5)

Homework

Graph each equation

22. y – 2 = (x + 4)23. y + 5 = -2(x – 4)24. y – 1 = 4(x – 2)

25. y – 5 = - 13

(x – 1)

26. y – 0 = 15

(x – 3)

Graph using intercepts

Classwork

Rewrite the equations in standard form. Graph the intercepts and then the line that passes through them.

27. y = 3x + 428. y = -2x + 329. y = x + 7

30. y = 25x – 2

31. y = - 3x

32. y = - 23x + 5

33. y – 4 = 2(x – 5)34. y + 5 = -3(x – 4)

35. y + 6 = 14 (x – 6)

36. y – 3 = (x + 7)

Homework

Rewrite the equations in standard form. Graph the intercepts and then the line that passes through them.

37. y = 6x + 4

38. y = -3x – 2

39. y = 16x – 3

40. y = x + 4

41. y = - 27x – 2

42. y = -7x43. y – 5 = 2(x – 3)44. y + 2 = -4(x – 2)

45. y – 3 = 37

(x – 3)

46. y + 1 = 2(x + 1)

Slope Formula

Classwork

Find the slope of the line through each of the following two points.

47. (-12,-5), (0,-8)48. (12,-18),(11,12)49. (-18,-20),(-18,-15)50. (-20,-4),(-12,-10)51. (8,10),(0,14)52. (6,9),(3,-9)53. (1,2),(5,7)54. (3,-3),(12,-2)55. (-4,-8),(-1,1)56. (4,7),(-3,7)

Homework

Find the slope of the line through each of the following two points.

57. (3,-9),(1,1)58. (7,4),(3,8)59. (-3,0),(5,12)60. (8,-2),(12,-2)61. (6,-3),(2,9)62. (-3,7),(-4,8)63. (5,9),(5,-8)64. (-5, 0.5),(-6,3)65. (-7,1),(7,8)66. (-2,1),(5,7)

Horizontal & Vertical Lines

Classwork

Determine if the following equations are horizontal, vertical, neither or cannot be determined.

67. y = -568. x = 769. 2x + 4y = 8

70. 7x – 21 = 071. 3x + 2y = 3x – 4

Homework

Determine if the following equations are horizontal, vertical, neither or cannot be determined.

72. x = -573. y = 774. 8x + -4y = -275. -6x – 3y = -6x + 276. -8x = -24

Parallel and Perpendicular Lines

Classwork

Match the following parallel equations from each column.

77. y = 3x – 2 78. y = -2x + 1

79. y = 13x – 7

80. 6x – 2 = 7y

81. 2(y + x) = 1882. 3y = x + 1883. -4x + 17 = 2y84. 6y + x = 085. -5(3y – 9x) = 3086. 14y = 12x + 28

Match the following perpendicular equations from each column.

87. y = -4x – 488. 2y = 3x + 1289. 7x + y = -10

90. y – 5 = 12

(x + 4)

91. 3(4y + 8x) = 0

92. y + 3 = -2(x – 5)93. 4y = x – 494. 2x = 14y -8

95. y + 4 = 12

(x – 4)

96. 2x + 3y = 15

97. Write an equation that would be parallel to the line y = 4x + 7

98. Write an equation that would be perpendicular to the line 4x + 6y = -12

Homework

Match the following parallel equations from each column.

99. y = 3x+ 7100. 4y = 16x + 12101. 6x + 12y = 1

102. y – 4 = 45

(x – 11)

103. 0 = 22x – 11y104. 24x – 6y = 18105. y + 5 = 2(x – 13)106. 2y + x = 24107. 3(15y – 12x) = 27108. -12x = -4y – 16

Match the following perpendicular equations from each column.

109. 6y = -12x + 9

110. y – 4 = 15

(x + 7)

111. 5(2x – 8y) = 35112. 35x – 5y = 0

113. 19 + y = -3x114. y – 9 = -4(x – 2)115. 3x + 21y = 0116. 8(14y – 7x) = 24117. y = -5x + 5118. -10x + 30y + 20 = 0

119. Write an equation that would be parallel to the line 6y = -24y – 18

120. Write an equation that would be perpendicular to the line y – 4 = 25

(x + 4)

How to write equations from given information

Classwork

121. Write an equation in point slope form for the line through the given point with the given slope.a. (3,4); m = 6

b. (-2,-7); m = - 32

c. (7,-4); m = -3d. (4,0); m = 1

e. (-4,-4); m = 13

122. A line passes through the given points. First write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form.

a. (-1,0), (1,2)b. (3,5), (0,0)c. (6,-2), (9,-8)d. (-1,-5), (-7,-6)e. (-3,4), (3,-2)

123. Write the equation of the line through the given points in standard form.a. (6,3), (-4, 2)b. (12,3), (-8,-4)c. (15,-4), (8, -3)d. (7,2), (8,5)e. (20,-10), (-30, 0)

124. A line has an x-intercept of 8 and y-intercept of 12.a. Write an equation for the line.b. Write an equation that is parallel to this line.c. Write an equation that is perpendicular to the line from part a.

125. Write the equation of the line through (-3,-2) and is parallel to the line y = -2x + 5

126. Write the equation of the line through (7,4) and perpendicular to y = 12

x – 5

Homework

127. Write an equation in point slope form for the line through the given point with the given slope.a. (5,-4); m = -2b. (-2, -3); m = 4

c. (7,4); m = 14

d. (9,-9); m = 3

e. (6,0); m = - 23

128. A line passes through the given points. First write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form.

a. (-10,-50), (5,25)b. (0,10), (10,-20)c. (0.5,9), (50,-90)d. (8,9), (5,-6)e. (-7, 4), (-3,6)

129. Write the equation of the line through the given points in standard form.a. (1,4), (-1,1)b. (5,-3), (3,4)c. (2,4), (-3,-6)d. (5,3), (4,5)e. (0,0), (-1,-2)

130. A line has an x-intercept of -4 and y-intercept of 16.a. Write an equation for the line.b. Write an equation that is parallel to this line.c. Write an equation that is perpendicular to the line from part a.

131. Write the equation of the line through (8,5) and is parallel to the line y = x + 7

132. Write the equation of the line through (-2,5) and perpendicular to y = - 23

x + 3

Answer Key1. (0, -4), (4/3, 0), (1, -1)2. (0, 4), (2, 0), (1, 2)3. (0, -3), (3, 0), (1, -2)4. (0, 4), (-8, 0), (1, 4.5)5. (0, 1), (3/2, 0), (1, 1/3)6. (0, -2), (-2, 0), (1, -3)7. (0, 1), (-.5, 0), (1, 3)8. (0, 0), (1, ¼), (2, ½)9. (0, -2), (-1, 0), (2, -6)10. (0, 4), (12, 0), (1, 11/3)11.

a. A(0, 0), B(0, 6), C(0, -5), D(0, -2)b. A: negative, B: positive, C: positive, D: zero

12. E: -1/2, F: -2, G: undefined, H: 113. E: -(x/2)+1, F: -2x+4, G: x=8, H: x-714.

a. I(0, 8), J(0, 2), K(0, -1), L(0, -8)b. I: zero, J: negative, K: positive, L: positive

15. M: -1, N: 3/2, O: 1, P: -1/316. M: -x+5, N: (3x)/2, O: y=-4, P: -(x/3)-6

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27. -3x + y = 4

28. 2x + y = 3

29. –x + y = 7

30. –(2/5)x + y = 0

31. 3x + y = 0

32. (2/3)x + y = 5

33. -2x + y = -6

34. 3x + y = 7

35. –(x/4) + y = -(15/2)

36. –x + y = 10

37. -6x + y = 4

38. 3x + y = -2

39. –(1/6)x + y = -3

40. –x + y = 4

41. (2/7)x + y = -2

42. 7x + y = 0

43. -2x + y = 2

44. 4x + y = 6

45. –(3/7)x + y = 12/7

46. -2x + y = 1

47. ¼48. -3049. Undefined50. -3/451. -1/252. 653. 5/454. 1/955. 356. 057. -1/558. -159. 3/260. 061. -362. -163. Undefined64. -5/265. ½66. 6/767. Horizontal68. Vertical69. Neither70. Vertical71. Horizontal72. Vertical73. Horizontal

74. Neither75. Horizontal76. Vertical77.

78.

79.

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81.

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83.

84.

85.

86.

87.

88.

89.

90.

91.

92.

93.

94.

95.

96.

97. Multiple Answers ex: y = 4x + 298. Multiple Answers ex: y = (6/4)x + 2

99.

100.

101.

102.

103.

104.

105.

106.

107.

108.

109.

110.

111.

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113.

114.

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118.

119. y = 1120. y = -(5/2)x + 4121.

a. y-4=6(x-3)b. y+7=-(3/2)(x+2)c. y+4=-3(x-7)d. y=x-4e. y+4=(1/3)(x+4)

122. a. y-1=x-2, y=x-1

b. y-5=(5/3)(x-3), y=(5/3)xc. y+8=-2(x-9), y=-2x+10d. y+6=(1/6)(x+7), y=(1/6)x-(29/6)e. y+2=-1(x-3), y=-x+1

123. a. –(x/10)+y=(12/5)b. –(7/20)x+y=-(6/5)c. (x/7)+y=-(13/7)d. -3x+y=-19e. (x/5)+y=14

124. a. y=-(3/2)x+12b. y=-(3/2)xc. y=(2/3)x+1

125. y=-2x+4126. y=-2x+18127.

a. y+4=-2(x-5)b. y+3=4(x+2)c. y-4=(1/4)(x-7)d. y+9=3(x-9)e. y=-(2/3)(x-6)

128. a. y+50=5(x+10), y=5xb. y-10=-3x, y=-3x+10c. y-9=-2(x-.5), y=-2x+10d. y-9=5(x-8), y=5x-31e. y-4=.5(x+7), y=.5x+(15/2)

129. a. –(3/2)x+y=-.5b. (7/2)x+y=14.5c. -2x+y=0d. 2x+y=13e. -2x+y=0

130. a. y=4x+16b. y=4x+4c. y=-(1/4)x+4

131. y=x-3132. y=(3/2)x+8