1. Graphing Lines and Linear Inequalities
Equations
Drive on The Education Highway

2. 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.

3. Parts of a coordinate plane.

4. Click on the correct quadrant numbers. Correct answer = applause.6 5
Quadrant
Quadrant 4 I II
III IV I II
III IV 3 2 1 -1
Quadrant
Quadrant -2 -3 I II
III IV I II
III IV -4 -5 -6
Lesson
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5. Click on the correct axis names. Correct answer = clapping.6 5 4 3 2 1
x-axis
y-axis -1 -2 -3 -4 -5 -6
x-axis
y-axis
Lesson
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6. Click on the point for the origin. Correct answer = clapping.6 5 4 3 2 1 x -1 -2 -3 -4 -5 -6
Lesson
Start y

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

8. You chose a line segment instead of a point.
Go back and try again.
INCORRECT ANSWER

9. INCORRECT ANSWER 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.
INCORRECT ANSWER

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

11. You did not choose an ordered pair.
Go back and try again.
INCORRECT ANSWER

12. INCORRECT ANSWER 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.
INCORRECT ANSWER

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

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

15. Slope is the slant of a line. Slope = rise change in y’s
What is slope?
Slope is the slant of a line.
Slope = rise change in y’s
run change in x’s
Slope is a fraction/integer.
Lesson
Start

16. 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. 5 4 9 1 2 3 4 5 6 7 8 6 3 5 2 4 1 3 x 2
2. Put that number on top of the fraction line. -1
Slope = 6 1 -2 9 -3 -4
3, Count the number of units to the right.
4. Put that number under the fraction line. y
Lesson
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17. How to determine the slope when the line goes down.
1. Count the number of units down from right point to left point. 5 4 -1 3 -2 2 -3 1 -4 x
2. Put that number on top of fraction line. -5 -1
Slope = -6 -6 2 1 3 -2 3 -3 -4
3. Count the units to the right. y
4. Put that number under the fraction line.
Lesson
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18. Determine the slope of the line shown.5 4 3 2 1 x -1 -2 -3 -4
-1/3
3/1 y
-3/1
1/3
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19. The line does not go down.
Go back and try again.
INCORRECT ANSWER
Lesson
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20. INCORRECT ANSWER The line does not rise 3 units,
then run 1 unit to the right.
Go back and try again.
INCORRECT ANSWER
Lesson
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21. Determine the slope of the line shown.5 4 3 2 1 x -1 -2 -3 -4
-2/3
3/2 y
-3/2
2/3
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22. INCORRECT ANSWER The line does not go up. Go back and try again.
Lesson
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23. INCORRECT ANSWER The line does not rise -2 units,
then run 3 units to the right.
Go back and try again.
INCORRECT ANSWER
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24. Slope Formula: m = (y1 - y2) (x1 - x2) where m = slope
and (x1, y1), (x2, y2) are
points on the line.
Lesson
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25. 1. Assign values as follows:
Example: Find the slope for a line with points (-3, 4) and (7, -2) on it.
1. Assign values as follows:
(x1, y1) = (-3, 4)
(x2, y2) = (7, -2)
2. Substitute them into the formula and solve.
m = 4 - (-2) = = -3
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26. Find the slope of the line with points (5, 6) and (2, 9) on it.
1. (x1, y1) =
(5, 6)
(2, 9)
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27. Find the slope of the line with points (5, 6) and (2, 9) on it.
1. (x1, y1) = (5, 6)
2. (x2, y2) =
(5, 6)
(2, 9)
Lesson
Start

28. Find the slope of the line with points (5, 6) and (2, 9) on it.
1. (x1, y1) = (5, 6)
2. (x2, y2) = (2, 9)
6 + 9
5 + 2
6 - 9
5 - 2
3. m =
5 - 2
6 - 9
5 + 2
6 + 9
Lesson
Start

29. The slope formula is a case of subtraction
on top and bottom.
Go back and try again.
INCORRECT ANSWER
Lesson
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30. INCORRECT ANSWER You have your x’s and y’s upside down. Remember:
“Y’s guys are always in the skies!”
Go back and try again.
INCORRECT ANSWER
Lesson
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31. INCORRECT ANSWER You have your x’s and y’s upside down.
You are also adding when you need to subtract.
Go back and try again.
INCORRECT ANSWER
Lesson
Start

32. Find the slope of the line with points (5, 6) and (2, 9) on it.
1. (x1, y1) = (5, 6)
2. (x2, y2) = (2, 9)
3. m = = -3 = -1
Lesson
Start

33. Find the slope of the line with points (7, 5) and (3, -4) on it. m =
5 - 4 = 1
= 4
5 - (-4) 9
5 - (-4) = 9
5 - (-4) = 9
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34. INCORRECT ANSWER You have your x’s and y’s upside down. Remember:
“Y’s guys are always in the skies!”
Go back and try again.
INCORRECT ANSWER
Lesson
Start

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

37. 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
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38. Positive and Negative Slopes.
Type Graph Algebra
Positive Up left to right. Positive
Fraction
SMILE
Negative Down left to right Negative
Fraction
Frown
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39. 2 Special Types of Slopes Type Graphs Algebra
Zero Horizontal Line 0/a, a  0
Why, o y, do I look upon the horizon?
Undefined Vertical Line a/0
No Slope
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40. Determining Types of Slopes by Looking at Graphs of Lines
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41. + - Is the slope of the line positive, negative, zero, or undefined? 5 4 3 2 1 x -1 -2 -3 -4 +  - y
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42. + - Is the slope of the line positive, negative, zero, or undefined? 5 4 3 2 1 x -1 -2 -3 -4 +  - y
Lesson
Start

43. + - Is the slope of the line positive, negative, zero, or undefined? 5 4 3 2 1 x -1 -2 -3 -4 +  - y
Lesson
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44. + - Is the slope of the line positive, negative, zero, or undefined? 5 4 3 2 1 x -1 -2 -3 -4 +  - y
Lesson
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45. Click on the line with the negative slope.5 4 3 2 1 x -1 -2 -3 -4 y
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46. Click on the line with the zero slope.5 4 3 2 1 x -1 -2 -3 -4 y
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47. Click on the line with the no slope.5 4 3 2 1 x -1 -2 -3 -4 y
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48. Click on the line with the positive slope.5 4 3 2 1 x -1 -2 -3 -4 y
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49. Determining Types of Slopes
Algebraically.
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50. Is the slope of the line with the 2 points listed positive, negative, zero, or undefined?
Points (-3, 5) and (-9, -4) + - 
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51. Is the slope of the line with the 2 points listed positive, negative, zero, or undefined?
Points (3, 5) and (3, -4) + - 
Lesson
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52. Is the slope of the line with the 2 points listed positive, negative, zero, or undefined?
Points (-3, -5) and (-9, -4) + - 
Lesson
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53. Is the slope of the line with the 2 points listed positive, negative, zero, or undefined?
Points (-3, -4) and (-9, -4) + - 
Lesson
Start

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

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

56. Slope-intercept Form:
y = mx + b
where m = slope
and b = y-intercept.
Lesson
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57. Example: y = -1/2x + 4 -1/2 = m = slope 4 = b = y-intercept Lesson
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58. Graphing by Slope-intercept
1. Graphing lines with
positive/negative slopes.
2. Graphing lines with zero or
undefined/no slopes.
Lesson
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59. 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

60. Graph y = -1/2x + 4
4. Draw a line through the 2 points you plotted.
1. Last number is 4, so go up 4 on the y-axis from the origin and plot a point.
2. Slope is already 2 numbers. Top one is -1, so go down 1 from the point you just plotted. 5 4 3 3 2 2 1 1 x -1
3. The bottom number is 2, so go 2 units to the right and plot a point. -2 -3 -4 y
Lesson
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61. Graph y = 2x - 3 1 1 2 4. Go 1 unit to the right and plot a point.
1. Last number is -3, so go down 3 units from the origin and plot a point.
2. The slope is only 1 number so put a 1 under the 2. 5 4 3 2 1 x 1 -1
3. Go up 2 from the point you just plotted.
5. Draw a line through the 2 points you plotted. 2 -2 -3 -4 y
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62. Click on the graph for y = 2/3x - 25 4 3 2 1 x -1 -2 -3 -4 y
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63. The slope is not negative.
Go back and try again.
INCORRECT ANSWER
Lesson
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64. You graphed the last number on the x-axis instead of the y-axis.
Go back and try again.
INCORRECT ANSWER
Lesson
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65. INCORRECT ANSWER Top number is 2, and the bottom is 3,
so you do not go up 3 and over 2.
Go back and try again.
INCORRECT ANSWER
Lesson
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66. Click on the graph for y = -4x + 35 4 3 2 1 x -1 -2 -3 -4 y
Lesson
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67. The slope is not positive.
Go back and try again.
INCORRECT ANSWER
Lesson
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68. INCORRECT ANSWER The -4 is not the y-intercept,
nor is the 3 the x-intercept.
Go back and try again.
INCORRECT ANSWER
Lesson
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69. The -4 is the slope, not the x-intercept.
Go back and try again.
INCORRECT ANSWER
Lesson
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70. Line with an undefined slope.
Two Special Graphs:
Line with a zero slope
And
Line with an undefined slope.
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71. “Why, o y, do I look upon the horizon?”
Line with a zero slope:
y = # (no x)
graphs as a horizontal line.
“Why, o y, do I look upon the horizon?”
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72. Graph the equation y = 2. x y Lesson Start 5 4 3 2 1 -1 -2 -3 -4 y
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73. Line with an undefined/no slope: x = # (no y)
graphs as a vertical line.
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74. Graph the equation x = -4. x y Lesson Start 5 4 3 2 1 -1 -2 -3 -4 y
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75. Click on the graph for x = 3.5 4 3 2 1 x -1 -2 -3 -4 y
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76. You chose the graph for x = -3.
Go back and try again.
INCORRECT ANSWER
Lesson
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77. The x = # (no y) line does not graph
as a horizontal line.
Go back and try again.
INCORRECT ANSWER
Lesson
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78. Click on the graph for y = -3½.5 4 3 2 1 x -1 -2 -3 -4 y
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79. The y = # (no x) line does not graph
as a vertical line.
Go back and try again.
INCORRECT ANSWER
Lesson
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80. You chose the graph for y = 3½.
Go back and try again.
INCORRECT ANSWER
Lesson
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81. 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
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82. Substitute the slope and the y-intercept
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 The new equation
Lesson
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83. 1. Click on the correct equation for a line with
slope = 5/3 and y-intercept = 2.
5/3y = 2x
y = 2x + 5/3
y = 5/3x + 2
y = -5/3x + 2
2. Click on the correct slope and y-intercept
pair for y = 7x - 5.
m = 7, b = -5
m = -5, b = 7
m = -7, b = 5
m = 1/7, b = -5
Lesson
Start

84. 1. Substitute the x, y, and m in the slope-intercept form.
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

85. 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.
2. Solve for b.
3 = -2 + b
+2 +2
5 = b
3. Substitute the slope and b in the equation.
y = -¼x + 5
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86. 1. Click on the correct substitution for a line
with slope = 1/3 and point (5, 9).
9y = 5x + 1/3
9 = 1/3x + 5
9 = 1/3(5) + b
5 = 1/3(9) + b
2. Click on the correct equation for a line
with slope = -2/3 and point (-6, 4).
y = -2/3x - 6
y = -2/3
Y = -2/3x + 4
y = -2/3x
Lesson
Start

87. 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

88. Continued on next screen.
Example: Write and equation for a
line with points (3, 7) & (5, 12).
m = (y1 - y2)
(x1 - x2)
m = = -5 = 5
1. Find the slope of the line.
Continued on next screen.
Lesson
Start

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

90. 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

91. 1. Click on the slope for a line with points (-2, 8) and (7, -5).3 -9 13 -9 -9 13 13 9
2. Click on the y-intercept for a line with
points (-2, 8) and (7, -5). 86 9 -5 86 13 46 9
Lesson
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92. 3. Click on the correct equation for a line
with points (3, 7) and (4, 8).
y = 3x + 7
y = 3/4x + 8
y = x + 4
y = -x + 4
Lesson
Start

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

94. 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-intercept x
y-intercept y

95. 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
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96. 1. Cover the x term and solve for y.
Graph the line for 3x + 2y = 6.
1. Cover the x term and solve for y.
3x + 2y = 6.
2. Go up 3 units on the y-axis.
5. Draw a line through the points plotted. 5 4 3 2 2
y = 3 1 1 x 1
3. Cover the y term and solve for x.
3x + 2y = 6.
4. Go right 2 units on the x-axis. -1 -2 -3 -4
x = 2 y
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97. 1. Click on the correct intercepts for 3x - 4y = 24.
x-int: 8
y-int: 6
x-int: 8
y-int: -6
x-int: 6
y-int: 8
x-int: -6
y-int: 8
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98. 2. Click on the graph of 3x - 6y = 12.5 4 3 2 1 x -1 -2 -3 -4 y
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99. 3. Click on the correct equation for the line shown.5
-9y - 6x
= -36 4
4x + 6y
= 36 3 2 1 x -1
6y + 4x
= 36
-6x - 9y
= -36 -2 -3 -4 y
Lesson
Start

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

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

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

103. Choose the type of line for the inequality given.
1. y > 3x - 2
a. Solid b. Dotted
2. y > ¼x - 5
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104. Choose the inequality symbol for the line shown.
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105. Choose the inequality symbol for the line shown.
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106. For Positive, Negative, & Zero Slopes
Where to Shade
For Positive, Negative, & Zero Slopes
For Undefined
or No Slopes

107. Where to Shade for Positive, Negative, and Zero Slopes:
The inequality must be in
y  mx + b
format.
 can be:
>, >, <, or <.
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108. If the inequality is: Shade y > mx + b or Above the line
Below the line
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109. Graph y > x - 2. 1. Graph the line y = x - 2. x
2. Since y >, shade above the line. y
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110. Graph y < x - 2. 1. Graph the line y = x - 2. x
2. Since y <, shade below the line. y
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111. Do you do anything different when the line is dotted rather than solid?
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112. Not Really
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113. Graph y > x - 2. 1. Graph the line
y = x - 2, but make the line dotted. x
2. Since y >, shade above the line. y
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114. Graph y < x - 2. 1. Graph the line
y = x - 2, but make the line dotted. x
2. Since y <, shade below the line. y
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115. Graph y > -½x + 3
Type of line:
Solid
Dotted x y
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116. Graph y > -½x + 3 Type of line: Solid Dotted x Shade ___ the line.
Above
Below
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117. Graph y > -½x + 3 Type of line: Solid Dotted x Shade ___ the line.
Above
Below
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118. Choose the correct inequality for the graph shown.
y < 1/3 x + 2
y < 1/3 x + 2 x
y > 1/3 x + 2
y > 1/3 x + 2 y
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119. Where to Shade for Undefined or No Slopes:
The inequality must be in
x  # (no y)
format.
 can be:
>, >, <, or <.
Lesson
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120. If the inequality is: Shade To the x > # or Right of the line
Left of the line
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121. Graph x > -2 1. Draw a dotted vertical line at x = -2. x
2. Shade to the right of the line. y
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122. Graph x < -2. 1. Graph the line X = -2. x
2. Shade to the left of the line. y
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123. Graph x > 3.
Choose type of line.
Solid
Dotted x y
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124. Graph x > 3. Choose type of line. Solid Choose where to shade. Left
Right y
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125. Graph x > 3. Choose type of line. Solid Choose where to shade.
Right y
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126. 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.
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127. Solve -3x - 2y < 12. -3x - 2y < 12 +3x +3x -2y < 3x + 12
y < -3/2 x - 6
>
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128. Choose the correct inequality. 1. 2x + 5y > -10
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