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 <= 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.