2. Linear Equations Linear Inequalities Drive on The Education Highway

3. Linear Equations and Graphing 1. Parts of a Coordinate Plane 2. Slope 3. Slope-intercept Form of a Linear Equation 4. Graphing by x- & y-intercepts.

4. Parts of a coordinate plane.

5. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 6 5 4 3 2 1 -2 -3 -4 -5 -6 Click on the correct quadrant numbers. Correct answer = applause. Quadrant IIIIIIIV Quadrant IIIIIIIV Quadrant IIIIIIIV Quadrant IIIIIIIV Lesson Start

6. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 6 5 4 3 2 1 -2 -3 -4 -5 -6 Click on the correct axis names. Correct answer = clapping. x-axis y-axis x-axisy-axis Lesson Start

7. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 6 5 4 3 2 1 -2 -3 -4 -5 -6 Click on the point for the origin. Correct answer = clapping. x y Lesson Start

8. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 6 5 4 3 2 1 -2 -3 -4 -5 -6 Click on point (-3, 5). Correct point = applause. x y Lesson Start

9. You chose a line segment instead of a point. Go back and try again.

10. You chose point (5, -3). Each ordered pair is in the form (x, y) -- it follows the alphabet in its internal order. You find the x value first, then you find the y value. Where they meet is the point. Go back and try again.

11. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 6 5 4 3 2 1 -2 -3 -4 -5 -6 Click on the correct ordered pair for the black point. -5/4 (4, -5) (-5, 4) -4/5 x y Lesson Start

12. You did not choose an ordered pair. Go back and try again.

13. You chose the ordered pair for the pale green point. Remember: x comes before y in the alphabet and in an ordered pair. Go back and try again.

14. Return to Main Menu. Return to Prior Problem. Continue to Next Lesson.

15. Slopes 1. What is a slope? 2. Slope formula 3. Types of slopes

16. What is slope? Slope is the slant of a line. Slope = risechange in y’s runchange in x’s Slope is a fraction/integer. Lesson Start

17. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y How to determine the slope when the line goes up. 1. Count the number of units up from the right point to the left point. 1 2 3 4 5 6 2. Put that number on top of the fraction line. Slope = 6 3, Count the number of units to the right. 12345678 9 4. Put that number under the fraction line. 9 Lesson Start

18. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y How to determine the slope when the line goes down. 1. Count the number of units down from right point to left point. -2 -3 -4 -5 -6 2. Put that number on top of fraction line. Slope = -6 3. Count the units to the right. 1 2 3 4. Put that number under the fraction line. 3 Lesson Start

19. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Determine the slope of the line shown. -1/3 3/1 -3/11/3 Lesson Start

20. The line does not go down. Go back and try again. Lesson Start

21. The line does not rise 3 units, then run 1 unit to the right. Go back and try again. Lesson Start

22. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Determine the slope of the line shown. -2/33/2 -3/22/3 Lesson Start

23. The line does not go up. Go back and try again. Lesson Start

24. The line does not rise -2 units, then run 3 units to the right. Go back and try again. Lesson Start

25. Slope Formula: m = (y 1 - y 2 ) (x 1 - x 2 ) where m = slope and (x 1, y 1 ), (x 2, y 2 ) are points on the line. Lesson Start

26. Example: Find the slope for a line with points (-3, 4) and (7, -2) on it. 1. Assign values as follows: 2. Substitute them into the formula and solve. m = 4 - (-2) = 6 = -3 -3 - 7 -10 5 (x 1, y 1 ) = (-3, 4) (x 2, y 2 ) = (7, -2) Lesson Start

27. Find the slope of the line with points (5, 6) and (2, 9) on it. 1. (x 1, y 1 ) = (5, 6)(2, 9) Lesson Start

28. Find the slope of the line with points (5, 6) and (2, 9) on it. 1. (x 1, y 1 ) = (5, 6) 2. (x 2, y 2 ) = (5, 6)(2, 9) Lesson Start

29. Find the slope of the line with points (5, 6) and (2, 9) on it. 1. (x 1, y 1 ) = (5, 6) 2. (x 2, y 2 ) = (2, 9) 3. m = 6 + 9 5 + 2 6 - 9 5 - 2 6 - 9 5 + 2 6 + 9 Lesson Start

30. The slope formula is a case of subtraction on top and bottom. Go back and try again. Lesson Start

31. You have your x’s and y’s upside down. Remember: “Y’s guys are always in the skies!” Go back and try again. Lesson Start

32. You have your x’s and y’s upside down. You are also adding when you need to subtract. Go back and try again. Lesson Start

33. Find the slope of the line with points (5, 6) and (2, 9) on it. 1. (x 1, y 1 ) = (5, 6) 2. (x 2, y 2 ) = (2, 9) 3. m = 6 - 9 = -3 = -1 5 - 2 3 Lesson Start

34. Find the slope of the line with points (7, 5) and (3, -4) on it. m = 5 - 4 = 1 7 - 3 4 7 - 3 = 4 5 - (-4) 9 5 - (-4) = 9 3 - 7 -4 5 - (-4) = 9 7 - 3 4 Lesson Start

35. You have your x’s and y’s upside down. Remember: “Y’s guys are always in the skies!” Go back and try again. Lesson Start

36. It is not 5 - 4, it is 5 - (-4). Go back and try again. Lesson Start

37. You must start with the y and x from the first point and end with the y and x from the second point. Go back and try again. Lesson Start

38. Types of Slopes: 1. Positive and Negative Slopes 2. Special Types of Slopes 3. Determining Types of Slopes by Looking at Graphs of Lines 4. Determining Types of Slopes Algebraically. Lesson Start

39. Positive and Negative Slopes. TypeGraph Algebra PositiveUp left to right.Positive Fraction NegativeDown left to right. Negative Fraction Lesson Start

40. 2 Special Types of Slopes TypeGraphsAlgebra ZeroHorizontal Line 0/a, a  0 UndefinedVertical Line a/0 No Slope Lesson Start

41. Determining Types of Slopes by Looking at Graphs of Lines Lesson Start

42. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Is the slope of the line positive, negative, zero, or undefined? - 0  + Lesson Start

43. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Is the slope of the line positive, negative, zero, or undefined? - 0  + Lesson Start

44. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Is the slope of the line positive, negative, zero, or undefined? - 0  + Lesson Start

45. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Is the slope of the line positive, negative, zero, or undefined? - 0  + Lesson Start

46. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Click on the line with the negative slope. Lesson Start

47. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Click on the line with the zero slope. Lesson Start

48. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Click on the line with the no slope. Lesson Start

49. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Click on the line with the positive slope. Lesson Start

50. Determining Types of Slopes Algebraically. Lesson Start

51. Is the slope of the line with the 2 points listed positive, negative, zero, or undefined? Points (-3, 5) and (-9, -4) +-0  Lesson Start

52. Is the slope of the line with the 2 points listed positive, negative, zero, or undefined? Points (3, 5) and (3, -4) +-0  Lesson Start

53. Is the slope of the line with the 2 points listed positive, negative, zero, or undefined? Points (-3, -5) and (-9, -4) +-0  Lesson Start

54. Is the slope of the line with the 2 points listed positive, negative, zero, or undefined? Points (-3, -4) and (-9, -4) +-0  Lesson Start

55. Return to Main Menu. Return to Prior Problem. Continue to Next Lesson.

56. Slope-intercept Form of a Linear Equation 1. Slope-intercept equation 2. Graphing by slope-intercept 3. Writing slope-intercept equations

57. Slope-intercept Form: y = mx + b where m = slope and b = y-intercept. Lesson Start

58. Example: y = -1/2x + 4 -1/2 = m = slope 4 = b = y-intercept Lesson Start

59. Graphing by Slope-intercept 1. Graphing lines with positive/negative slopes. 2. Graphing lines with zero or undefined/no slopes. Lesson Start

60. The Slope-intercept Song You make the last number first. It’s either up or down. Make the slope in 2 numbers, Or you look like a clown. Top one’s up or down, And the bottom’s always right. You’d better do it well, Or you’ll get a fright. (Tune: “Hokey-Pokey”) Lesson Start

61. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Graph y = -1/2x + 4 1. Last number is 4, so go up 4 on the y- axis from the origin and plot a point. 1 2 3 2. Slope is already 2 numbers. Top one is -1, so go down 1 from the point you just plotted. 3. The bottom number is 2, so go 2 units to the right and plot a point. 4. Draw a line through the 2 points you plotted. Lesson Start

62. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Graph y = 2x - 3 1. Last number is -3, so go down 3 units from the origin and plot a point. 1 2 2. The slope is only 1 number so put a 1 under the 2. 3. Go up 2 from the point you just plotted. 4. Go 1 unit to the right and plot a point. 5. Draw a line through the 2 points you plotted. 1 Lesson Start

63. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Click on the graph for y = 2/3x - 2 Lesson Start

64. The slope is not negative. Go back and try again. Lesson Start

65. You graphed the last number on the x-axis instead of the y-axis. Go back and try again. Lesson Start

66. Top number is 2, and the bottom is 3, so you do not go up 3 and over 2. Go back and try again. Lesson Start

67. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Click on the graph for y = -4x + 3 Lesson Start

68. The slope is not positive. Go back and try again. Lesson Start

69. The -4 is not the y-intercept, nor is the 3 the x-intercept. Go back and try again. Lesson Start

70. The -4 is the slope, not the x-intercept. Go back and try again. Lesson Start

71. Two Special Graphs: Line with a zero slope And Line with an undefined slope. Lesson Start

72. Line with a zero slope: y = # (no x) graphs as a horizontal line. “Why, o y, do I look upon the horizon?” Lesson Start

73. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Graph the equation y = 2. Lesson Start

74. Line with an undefined/no slope: x = # (no y) graphs as a vertical line. Lesson Start

75. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Graph the equation x = -4. Lesson Start

76. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Click on the graph for x = 3. Lesson Start

77. You chose the graph for x = -3. Go back and try again. Lesson Start

78. The x = # (no y) line does not graph as a horizontal line. Go back and try again. Lesson Start

79. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Click on the graph for y = -3½. Lesson Start

80. The y = # (no x) line does not graph as a vertical line. Go back and try again. Lesson Start

81. You chose the graph for y = 3½. Go back and try again. Lesson Start

82. Writing Slope-intercept Equations: 1. When given a slope and the y-intercept. 2. When given a slope and one point on the line. 3. When given 2 points on the line. m = ¾, b = -1 m = -¼, (8, 3) (3, 7), (5, 12) Lesson Start

83. Writing a slope-intercept equation when given a slope and the y-intercept. Substitute the slope and the y-intercept for the m and b in the equation. Example: m = ¾, b = -1 y = mx + b Slope-int. equation y = ¾x - 1 The new equation Lesson Start

84. 1. Click on the correct equation for a line with slope = 5/3 and y-intercept = 2. y = 5/3x + 2y = 2x + 5/35/3y = 2xy = -5/3x + 2 2. Click on the correct slope and y-intercept pair for y = 7x - 5. m = 7, b = -5m = -5, b = 7m = -7, b = 5m = 1/7, b = -5 Lesson Start

85. Writing a slope-intercept equation when given a slope and a point on the line. 1. Substitute the x, y, and m in the slope-intercept form. 2. Solve for b. 3. Substitute the slope and the b in a clean slope-intercept form. Lesson Start

86. Example: Write the equation of the line with slope = -¼ and point (8, 3). y = mx + b 3 = -¼(8) + b 1. Substitute the slope, x, and y in the equation. 3 = -2 + b +2 5 = b 2. Solve for b. y = -¼x + 5 3. Substitute the slope and b in the equation. Lesson Start

87. 1. Click on the correct substitution for a line with slope = 1/3 and point (5, 9). 9 = 1/3(5) + b5 = 1/3(9) + b9 = 1/3x + 59y = 5x + 1/3 2. Click on the correct equation for a line with slope = -2/3 and point (-6, 4). y = -2/3xY = -2/3x + 4y = -2/3y = -2/3x - 6 Lesson Start

88. Writing a slope-intercept equation for a line with 2 points given: 1. Find the slope of the line. 2. Use that slope and the first point to find the y-intercept. 3. Substitute the slope and the y-intercept into the equation. Lesson Start

89. Example: Write and equation for a line with points (3, 7) & (5, 12). 1. Find the slope of the line. m = (y 1 - y 2 ) (x 1 - x 2 ) m = 7 - 12 = -5 = 5 3 - 5 -2 2 Continued on next screen. Lesson Start

90. Write and equation for a line with points (3, 7) & (5, 12). m = 5/2 y = mx + b 2. Use the slope and the first point to solve for the y-intercept. 7 = (5/2)(3) + b 2(7) = 2(15/2) + 2b 14 = 15 + 2b -15 -15 -1 = 2b  -1/2 = b 2 2 Continued on next screen. Lesson Start

91. Write and equation for a line with points (3, 7) & (5, 12). m = 5/2, b = -1/2 3. Substitute the slope and the y-intercept for the m and the b in the equation. y = mx + b y = 5/2x - 1/2 Lesson Start

92. 1. Click on the slope for a line with points (-2, 8) and (7, -5). 13 -9 3 -9 13 9 2. Click on the y-intercept for a line with points (-2, 8) and (7, -5). 46 9 86 9 -5 86 13 Lesson Start

93. 3. Click on the correct equation for a line with points (3, 7) and (4, 8). y = x + 4 y = 3x + 7 y = -x + 4 y = 3/4x + 8 Lesson Start

94. Return to Main Menu. Return to Prior Problem. Continue to Next Lesson.

95. Graphing by x- and y-intercepts. X-intercept: where the line crosses the x-axis. Y-intercept: where the line crosses the y-axis. x y x-intercept y-intercept

96. How to graph by x- & y-intercepts: 1. Cover the x term with your index finger and solve the resulting equation for y. 2. Go up or down on the y-axis from the origin that many units and plot a point. 3. Cover the y term with your index finger and solve the resulting equation for x. 4. Go left or right on the x-axis from the origin that many units and plot a point. 5. Draw a line through your points. Lesson Start

97. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y Graph the line for 3x + 2y = 6. 1. Cover the x term and solve for y. 3x + 2y = 6. y = 3 2. Go up 3 units on the y-axis. 1 2 3. Cover the y term and solve for x. 3x + 2y = 6. x = 2 4. Go right 2 units on the x-axis. 1 5. Draw a line through the points plotted. Lesson Start

98. 1. Click on the correct intercepts for 3x - 4y = 24. x-int: 8 y-int: -6 x-int: -6 y-int: 8 x-int: 8 y-int: 6 x-int: 6 y-int: 8 Lesson Start

99. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y 2. Click on the graph of 3x - 6y = 12. Lesson Start

100. -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 5 4 3 2 1 -2 -3 -4 x y 3. Click on the correct equation for the line shown. -6x - 9y = -36 -6x - 9y = -36 -9y - 6x = -36 -9y - 6x = -36 4x + 6y = 36 4x + 6y = 36 6y + 4x = 36 6y + 4x = 36 Lesson Start

101. Return to Main Menu. Return to Prior Problem. Continue to Next Lesson.

102. Graphing Linear Inequalities Type of Line Where to Shade Solving Inequalities

103. How to Determine the Type of Line to Draw Inequality Symbol Type of Line > or <Dotted Line > or <Solid Line

104. Choose the type of line for the inequality given. 1. y > 3x - 2 a. Solidb. Dotted 2. y > ¼x - 5 a. Solidb. Dotted Lesson Start

105. Choose the inequality symbol for the line shown. < or > < or > Lesson Start

106. Choose the inequality symbol for the line shown. < or > < or > Lesson Start

107. For Positive, Negative, & Zero Slopes For Undefined or No Slopes

108. Where to Shade for Positive, Negative, and Zero Slopes: The inequality must be in y  mx + b format.  can be: >, >, <, or <. Lesson Start

109. If the inequality is: Shade y > mx + b or y > mx + b Above the line y < mx + b or y < mx + b Below the line Lesson Start

110. x y Graph y > x - 2. 1. Graph the line y = x - 2. 2. Since y >, shade above the line. Lesson Start

111. x y Graph y < x - 2. 1. Graph the line y = x - 2. 2. Since y <, shade below the line. Lesson Start

112. Do you do anything different when the line is dotted rather than solid? Lesson Start

113. Lesson Start

114. x y Graph y > x - 2. 2. Since y >, shade above the line. 1. Graph the line y = x - 2, but make the line dotted. Lesson Start

115. x y Graph y < x - 2. 1. Graph the line y = x - 2, but make the line dotted. 2. Since y <, shade below the line. Lesson Start

116. x y Graph y > -½x + 3 Type of line: Solid Dotted Lesson Start

117. x y Graph y > -½x + 3 Type of line: Solid Dotted Shade ___ the line. AboveBelow Lesson Start

118. x y Graph y > -½x + 3 Type of line: Solid Dotted Shade ___ the line. AboveBelow Lesson Start

119. x y Choose the correct inequality for the graph shown. y < 1/3 x + 2 y < 1/3 x + 2 y > 1/3 x + 2 y > 1/3 x + 2 Lesson Start

120. Where to Shade for Undefined or No Slopes: The inequality must be in x  # (no y) format.  can be: >, >, <, or <. Lesson Start

121. If the inequality is: Shade To the x > # or x > # Right of the line x < # or x < # Left of the line Lesson Start

122. x y Graph x > -2 1. Draw a dotted vertical line at x = -2. 2. Shade to the right of the line. Lesson Start

123. x y Graph x < -2. 1. Graph the line X = -2. 2. Shade to the left of the line. Lesson Start

124. x y Graph x > 3. Choose type of line. Solid Dotted Lesson Start

125. x y Graph x > 3. Choose type of line. Solid Choose where to shade. Left Right Lesson Start

126. x y Graph x > 3. Choose type of line. Solid Choose where to shade. Right Lesson Start

127. Solving Inequalities You use the same algebraic methods as solving equations except when you multiply/divide both sides by the same negative number. In that case, you switch the direction of the inequality symbol. Lesson Start

128. Solve -3x - 2y < 12. -3x - 2y < 12 +3x -2y < 3x + 12 -2 -2-2 y < -3/2 x - 6> Lesson Start

129. Choose the correct inequality. 1. 2x + 5y > -10 y > -2/5 x - 2 y < -2/5 x - 2 y > 2/5 x + 2 y < 2/5 x + 2 2. 3x - 2y > 10 y > -2/3 x - 5 y < -2/3 x - 5 y > 2/3 x - 5 y < 2/3 x - 5 Lesson Start