1. Graphing Linear Inequalities in Two Variables
Objective: Graph all of the solutions to a linear inequality
NCSCOS: 1.02, 3.03, 4.01

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 <= or >=
Dotted if < or >
Shade above or below the line
Above if > or >=
Below if < or <=

3. Example 1
Graph y > 2x -5
The equation is already in slope-intercept form.
Start by plotting the y-intercept (b = -5)

4. Example 1 (cont) Graph y > 2x -5
Now use the slope to find other points on the line

5. Example 1 (cont) Graph y > 2x -5
Draw a dotted or solid line through the coordinates.
This line will be dotted since the inequality is >

6. Example 1 (cont) Graph y > 2x -5
Shade above the line to show all of the coordinates that are solutions.

7. Example 2 Graph 2x - 5y >=15 First, solve for y …
-5y >= -2x + 15
y <= 2/5 x – 3
Now go through the steps of graphing.

8. Example 2
Graph 2x - 5y >=15
y <= 2/5 x – 3
Plot the y-intercept

9. Example 2 Graph 2x - 5y >15 y <= 2/5 x – 3
Use the slope to find other points

10. Example 2 Graph 2x - 5y >15 y <= 2/5 x – 3
Draw a solid line through the points.

11. Example 2
Graph 2x - 5y >15
y <= 2/5 x – 3
Shade below the line

12. Special Example Graph x > 5
Remember the graph will be a vertical line.

13. Special Example Graph y< -2
Remember the graph will be a horizontal line.