1. Graphing in the Coordinate Plane

2. To graph ordered pairs of real numbers, we need a coordinate system.

3. Ordered Pairs
The rectangular or Cartesian coordinate system consists of a horizontal number line, the x-axis and a vertical number line, the y-axis as shown in the next slide.

4. x P (a,b) y - axis Quadrant II Quadrant I Origin Quadrant IV
Quadrant III
x - axis

5. y
Locate on the xy-plane the point corresponding to the ordered pair x

6. y
Locate on the xy-plane the point corresponding to the ordered pair (2,3) x

7. y
Locate on the xy-plane the point corresponding to the ordered pair (2,3) x

8. y
Locate on the xy-plane the point corresponding to the ordered pair (2,3)
(-2,-3) x

9. y
Locate on the xy-plane the point corresponding to the ordered pair (2,3)
(-2,-3) x

10. y
Locate on the xy-plane the point corresponding to the ordered pair (2,3)
(-2,-3)
(-1,3) x

11. y
Locate on the xy-plane the point corresponding to the ordered pair (2,3)
(-2,-3)
(-1,3) x

12. y
Locate on the xy-plane the point corresponding to the ordered pair (2,3)
(-2,-3)
(-1,3)
(0,-4) x

13. y
Locate on the xy-plane the point corresponding to the ordered pair (2,3)
(-2,-3)
(-1,3)
(0,-4) x

14. y
Locate on the xy-plane the point corresponding to the ordered pair (2,3)
(-2,-3)
(-1,3)
(0,-4)
(4,-2) x

15. y
Locate on the xy-plane the point corresponding to the ordered pair (2,3)
(-2,-3)
(-1,3)
(0,-4)
(4,-2) x

16. Ordered Pairs
An equation in two variables, such as y = 2x+3, is satisfied only if we find a value for x and a value for y that makes it true.

17. Ordered Pairs
2x + 3y = 6

18. For example, if x = 6 and y = -2, then the equation becomes
Ordered Pairs
2x + 3y = 6
For example, if x = 6 and y = -2, then the equation becomes

19. For example, if x = 6 and y = -2, then the equation becomes
Ordered Pairs
2x + 3y = 6
For example, if x = 6 and y = -2, then the equation becomes

20. For example, if x = 6 and y = -2, then the equation becomes
Ordered Pairs
2x + 3y = 6
For example, if x = 6 and y = -2, then the equation becomes

21. For example, if x = 6 and y = -2, then the equation becomes
Ordered Pairs
2x + 3y = 6
For example, if x = 6 and y = -2, then the equation becomes

22. For example, if x = 6 and y = -2, then the equation becomes
Ordered Pairs
2x + 3y = 6
For example, if x = 6 and y = -2, then the equation becomes

23. For example, if x = 6 and y = -2, then the equation becomes
Ordered Pairs
2x + 3y = 6
For example, if x = 6 and y = -2, then the equation becomes

24. For example, if x = 6 and y = -2, then the equation becomes
Ordered Pairs
2x + 3y = 6
For example, if x = 6 and y = -2, then the equation becomes

25. For example, if x = 6 and y = -2, then the equation becomes
Ordered Pairs
2x + 3y = 6
For example, if x = 6 and y = -2, then the equation becomes

26. Ordered Pairs
The order of the numbers in an ordered pair is important. For example, (3,0) also satisfies
2x + 3y = 6

27. Ordered Pairs
The order of the numbers in an ordered pair is important. For example, (3,0) also satisfies
2x + 3y = 6

28. Ordered Pairs
The order of the numbers in an ordered pair is important. For example, (3,0) also satisfies
2x + 3y = 6

29. Ordered Pairs
The order of the numbers in an ordered pair is important. For example, (3,0) also satisfies
2x + 3y = 6

30. Ordered Pairs
The order of the numbers in an ordered pair is important. For example, (3,0) also satisfies
2x + 3y = 6

31. Ordered Pairs
The order of the numbers in an ordered pair is important. For example, (3,0) also satisfies
2x + 3y = 6

32. Ordered Pairs
The order of the numbers in an ordered pair is important. For example, (3,0) also satisfies
2x + 3y = 6

33. Ordered Pairs
The order of the numbers in an ordered pair is important. For example, (3,0) also satisfies
2x + 3y = 6

34. Ordered Pairs
2x + 3y = 6
However, (5,1) does not.

35. Ordered Pairs
2x + 3y = 6
However, (5,1) does not.

36. Ordered Pairs
2x + 3y = 6
However, (5,1) does not.

37. Ordered Pairs
2x + 3y = 6
However, (5,1) does not.

38. Ordered Pairs
2x + 3y = 6
However, (5,1) does not.

39. Ordered Pairs
2x + 3y = 6
However, (5,1) does not.

40. Ordered Pairs
2x + 3y = 6
However, (5,1) does not.

41. Ordered Pairs
2x + 3y = 6
However, (5,1) does not.

42. Ordered Pairs
2x + 3y = 6
However, (5,1) does not.

43. Ordered Pairs
2x + 3y = 6
However, (5,1) does not.

44. Ordered Pairs
In the ordered pair, the value for x is always written first and the value for y second:

45. Ordered Pairs
In the ordered pair, the value for x is always written first and the value for y second:

46. Ordered Pairs
In the ordered pair, the value for x is always written first and the value for y second:

47. Graphing a Linear Equation
2x + 3y = 6 y x

48. Graphing a Linear Equation
2x + 3y = 6 y x

49. Graphing a Linear Equation
2x + 3y = 6 y x

50. Graphing a Linear Equation
2x + 3y = 6 y x

51. Graphing a Linear Equation
2x + 3y = 6 y x

52. Graphing a Linear Equation
2x + 3y = 6 y x

53. Graphing a Linear Equation
2x + 3y = 6 y x

54. Graphing a Linear Equation
2x + 3y = 6 y x

55. Graphing a Linear Equation
2x + 3y = 6 y x

56. Graphing a Linear Equation
2x + 3y = 6 y x

57. Graphing a Linear Equation
2x + 3y = 6 y x

58. Graphing a Linear Equation
2x + 3y = 6 y x

59. Graphing a Linear Equation
2x + 3y = 6 y x

60. Graphing a Linear Equation
2x + 3y = 6 y x

61. Graphing a Linear Equation
2x + 3y = 6 y x

62. Graphing a Linear Equation
2x + 3y = 6 y x

63. Graphing a Linear Equation
2x + 3y = 6 y x

64. Graphing a Linear Equation
2x + 3y = 6 y x

65. Graphing a Linear Equation
2x + 3y = 6 y x

66. Graphing a Linear Equation
2x + 3y = 6 y x

67. Graphing a Linear Equation
2x + 3y = 6 y x

68. Linear Equation in Two Variables
A linear equation in two variables can be written in the form
Ax + By = C
where A, B, and C are real numbers.
this form is called standard form.

69. Use x and y intercepts.
Graph
4x - y = -3 y x

70. Use x and y intercepts.
Graph
4x - y = -3 y x

71. Use x and y intercepts.
Graph
4x - y = -3 y x

72. Use x and y intercepts.
Graph
4x - y = -3 y x

73. Use x and y intercepts.
Graph
4x - y = -3 y x

74. Use x and y intercepts.
Graph
4x - y = -3 y x

75. Use x and y intercepts.
Graph
4x - y = -3 y x

76. Use x and y intercepts.
Graph
4x - y = -3 y x

77. Use x and y intercepts.
Graph
4x - y = -3 y x

78. Use x and y intercepts.
Graph
4x - y = -3 y x

79. Use x and y intercepts.
Graph
4x - y = -3 y x

80. Use x and y intercepts.
Graph
4x - y = -3 y x

81. Use x and y intercepts.
Graph
4x - y = -3 y x

82. Use x and y intercepts.
Graph
4x - y = -3 y x

83. Use x and y intercepts.
Graph
4x - y = -3 y x

84. Use x and y intercepts.
Graph
4x - y = -3 y x

85. Use x and y intercepts.
Graph
4x - y = -3 y x

86. Use x and y intercepts.
Graph
4x - y = -3 y x

87. Use x and y intercepts.
Graph
4x - y = -3 y x

88. Use x and y intercepts.
Graph
4x - y = -3 y x

89. Use x and y intercepts.
Graph
4x - y = -3 y x

90. Use x and y intercepts.
Graph
4x - y = -3 y x

91. Use x and y intercepts.
Graph
4x - y = -3 y x

92. Use x and y intercepts.
Graph
4x - y = -3 y x

93. Use x and y intercepts.
Graph
4x - y = -3 y x

94. Use x and y intercepts.
Graph
4x - y = -3 y x

95. Use x and y intercepts.
Graph
4x - y = -3 y x

96. Use x and y intercepts.
Graph
4x - y = -3 y x

97. Use x and y intercepts.
Graph
4x - y = -3 y x

98. Graph y = 2 y x

99. Graph y = 2 y x

100. Graph y = 2 y x

101. Graph y = 2 y x

102. Graph y = 2 y x

103. Graph y = 2 y x

104. Graph y = 2 y x

105. Graph y = 2 y x

106. Graph y = 2 y x

107. Graph y = 2 y x

108. Graph y = 2 y x

109. Graph y = 2 y x

110. Graph y = 2 y x

111. Graph x+1 = 0 y
x = -1 x

112. Graph x+1 = 0 y
x = -1 x

113. Graph x+1 = 0 y
x = -1 x

114. Graph x+1 = 0 y
x = -1 x

115. Graph x+1 = 0 y
x = -1 x

116. Graph x+1 = 0 y
x = -1 x

117. Graph x+1 = 0 y
x = -1 x

118. Graph x+1 = 0 y
x = -1 x

119. Graph x+1 = 0 y
x = -1 x

120. Graph x+1 = 0 y
x = -1 x

121. Graph x+1 = 0 y
x = -1 x

122. Graph x+1 = 0 y
x = -1 x

123. Graph x+1 = 0 y
x = -1 x

124. Graph x+1 = 0 y
x = -1 x

125. y
Use Intercepts to Graph x

126. y
Use Intercepts to Graph x

127. y
Use Intercepts to Graph x

128. y
Use Intercepts to Graph x

129. y
Use Intercepts to Graph x

130. y
Use Intercepts to Graph x

131. y
Use Intercepts to Graph x

132. y
Use Intercepts to Graph x

133. y
Use Intercepts to Graph x

134. y
Use Intercepts to Graph x

135. y
Use Intercepts to Graph x

136. y
Use Intercepts to Graph x

137. y
Use Intercepts to Graph x

138. y
Use Intercepts to Graph x

139. y
Use Intercepts to Graph x

140. y
Use Intercepts to Graph x

141. y
Use Intercepts to Graph x

142. y
Use Intercepts to Graph x

143. y
Use Intercepts to Graph x

144. y
Use Intercepts to Graph x

145. y
Use Intercepts to Graph x

146. y
Use Intercepts to Graph x

147. Linear Equation in Two Variables