Start learning today, and be successful in your academic & professional career. Start Today!

Loading video...

### 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

1 answer

Last reply by: Catherine MOLAKAL

Wed Jul 27, 2016 6:30 PM

Post by Catherine MOLAKAL on July 27, 2016

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?