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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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For more information, please see full course syllabus of Algebra 1
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Lecture Comments (4)

1 answer

Last reply by: Catherine MOLAKAL
Wed Jul 27, 2016 6:30 PM

Post by Catherine MOLAKAL on July 27 at 06:28:45 PM

Dr Eathon,
how did you get -1 1/3 for -intercept, wont it be -4/3.

1 answer

Last reply by: Dr Carleen Eaton
Thu Jun 20, 2013 8:59 PM

Post by Taylor Wright on June 20, 2013

would it be easier to configure the equation in slope intercept form in order to determine the correct half plane?

Graphing Inequalities with Two Variables

  • The graph of an inequality in two variables is a half plane bounded by a straight line.
  • If the inequality is strict (< or >), then draw the boundary as a dashed line, otherwise draw it as a solid line.
  • Use a test point, normally the origin, to determine which half plane is the solution of the inequality. Shade that region.

Graphing Inequalities with Two Variables

Graph y > x - 2
  • Find slope and intercept
    b = - 2
    m = 1
  • Determine line type
  • Dashed since >
  • Test point (0,0)
    0 > 0 - 2
    0 > - 2
    Which is false
Graph utilizing properties
Graph y < 2x
  • Find slope and intercept
    b = 0
    m = 2
  • Determine line type
    Dashed since <
  • Test point (1,0)
    0 < 2(1)
    0 < 2
    Which is true
Graph utilizing properties
Graph y ≥ 5x + 1
  • Find slope and intercept
    b = 5m = 1
  • Determine line type
  • Solid since ≥
  • Test point (0,0)
    0 ≥ 5(0) + 1
    0 ≥ 1
    Which is false
Graph utilizing properties
Graph y ≥ [x/3] + 2
  • Find slope and intercept
    b = 2
    m = [1/3]
  • Determine line type
    Solid since
  • Test point (0,0)
    0 ≥ [0/3] + 2
    0 ≥ 2
    Which is false
Graph utilizing properties
Graph y ≤ x + 7
  • Find slope and intercept
    b = 7
    m = 1
  • Determine line type
  • Solid since £
  • Test point (0,0)
    0 ≤ 0 + 7
    0 ≤ 7
    Which is true
Graph utilizing properties
Graph y − x > 5
  • Find slope and intercept
    b = 5
    m = 1
  • Determine line type
  • Dashed since >
  • Test point (0,0)
    0 - 0 > 5
    0 > 5
    Which is false
Graph utilizing properties
Graph 2y + x < − 1
  • Find slope and intercept
    b = − 1
    m = − [1/2]
  • Determine line type
    Dashed since <
  • Test point (0,0)
    2(0) + 0 < - 1
    0 < - 1
    Which is false
Graph utilizing properties
Graph y + 2x > 3
  • Find 2 points using intercepts
    x = 0 → (0,3)y = 0 → (3,0)
  • Determine line type
    Dashed since >
  • Test point (0,0)
    0 + 2(0) > 3
    0 > 3
    Which is false
Graph utilizing properties
Graph 3y - x > - 5
  • Find 2 points using intercepts
    x = 0 → (0, − [5/3])y = 0 → (5,0)
  • Determine line type
    Dashed since >
  • Test point (0,0)
    3(0) - 0 > - 5
    0 > - 5
    Which is true
Graph utilizing properties
Graph [(4y + 5x)/2] ≤ 2
  • Find 2 points using intercepts
    x = 0 → (0,1)y = 0 → ([4/5],0)
  • Determine line type
    Solid since ≤
  • Test point (0,0)
    [(4(0) + 5(0))/2] ≤ 2
    [0/2] ≤ 2
    0 ≤ 2
    Which is true
Graph utilizing properties

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Graphing Inequalities with Two Variables

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Graph 0:08
    • Half Plane and Boundary
  • Technique for Graphing 1:57
    • Graph Equation
    • Solid Line or Dashed Line
    • Example
    • Choosing a Test Point
    • Example
  • Example 1: Solve the Inequality 7:49
  • Example 2: Solve the Inequality 11:37
  • Example 3: Solve the Inequality 15:44
  • Example 4: Solve the Inequality 19:10