Graphing Linear Inequalities in Two Variables

1
Graphing Linear Inequalities in Two Variables

• Objective Graph all of the solutions to a
  linear inequality

2
Steps to Remember

• Rewrite the inequality so that it is in
  slope-intercept form
• y mx b
• Plot the y-intercept (b)
• Use the slope (m) to find other points on the
  line.
• Draw the line
• Solid if lt or gt
• Dotted if lt or gt
• Shade above or below the line
• Above if gt or gt
• Below if lt or lt

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Example 1

• Graph y gt 2x -5
• The equation is already in slope-intercept form.
• Start by plotting the y-intercept (b -5)

4
Example 1 (cont)

• Graph y gt 2x -5
• Now use the slope to find other points on the line

5
Example 1 (cont)

• Graph y gt 2x -5
• Draw a dotted or solid line through the
  coordinates.
• This line will be dotted since the inequality is gt

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Example 1 (cont)

• Graph y gt 2x -5
• Shade above the line to show all of the
  coordinates that are solutions.

7
Example 2

• Graph 2x - 5y gt15
• First, solve for y
• -5y gt -2x 15
• y lt 2/5 x 3
• Now go through the steps of graphing.

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Example 2

• Graph 2x - 5y gt15
• y lt 2/5 x 3
• Plot the y-intercept

9
Example 2

• Graph 2x - 5y gt15
• y lt 2/5 x 3
• Use the slope to find other points

10
Example 2

• Graph 2x - 5y gt15
• y lt 2/5 x 3
• Draw a solid line through the points.

11
Example 2

• Graph 2x - 5y gt15
• y lt 2/5 x 3
• Shade below the line

12
Special Example

• Graph x gt 5
• Remember the graph will be a vertical line.

13
Special Example

• Graph ylt -2
• Remember the graph will be a horizontal line.