1. Graphing Linear Inequalities

2. Linear Inequalities LET’S REVIEW….
A linear equation in slope-intercept form is y = mx + b.
In this form, m represents the slope, and b is the y-intercept.
The solutions of a linear equation are points found on the line.

3. Linear Inequalities
A linear inequality has the same form except there is an inequality symbol instead of an equal sign.
The inequality symbols are:
< less than
> greater than
≤ less than or equal to
≥ greater than or equal to

4. How to Graph Linear Inequalities
Graphing linear inequalities is similar to graphing linear equations.
If the inequality is in slope-intercept form…
Identify the y-intercept and graph the it on the coordinate plane.
Identify the slope.
From the y-intercept, use the slope to identify another point.
Using those two points, graph the line.

5. How to Graph Linear Inequalities
Draw a CLOSED (solid) line connecting the points if the inequality has the ≤ or ≥ symbol.
The solution set is called a closed half plane.

6. How to Graph Linear Inequalities
Draw an OPEN (dotted/dashed) line connecting the points if the inequality has the < or > symbol.
The solution set is called an open half plane.

7. How to Graph Linear Inequalities
Now shade the area that includes the solution set.
If the inequality uses the symbol < or ≤, you will shade BELOW the line.
The solution(s) to the inequality are located in the shaded area BELOW the line.

8. How to Graph Linear Inequalities
If the inequality uses the symbol > or ≥, shade ABOVE the line.
The solution(s) to the inequality are located in the shaded area ABOVE the line.

9. How to Graph Linear Inequalities
Points that are solutions are found in the shaded areas.
If the linear inequality is drawn with a closed line, the points on the line ARE part of the solution set.
If the linear inequality is drawn with an open line, the points on the line ARE NOT part of the solution set.

10. Let’s try it together… Graph the following inequality: y< 3 x + 2
STEPS TO FOLLOW:
Identify and plot the y-intercept.
Use the slope to locate the next point. (rise over run)
Connect the points using a ruler.
Determine if the line should be closed or open.
Draw the line.
Determine if you need to shade above or below the line.

11. Dotted or dashed line and shading below the line.
Let’s try it together…
Graph the following inequality:
y< 3 x +2
Dotted or dashed line and shading below the line.

12. Solid line and shading below the line.
Let’s try it together…
Graph the following inequality:
y≤ 3 x +2
Solid line and shading below the line.

13. Dotted or dashed line and shading above the line.
Let’s try it together…
Graph the following inequality:
y> 3 x +2
Dotted or dashed line and shading above the line.

14. Solid line and shading above the line.
Let’s try it together…
Graph the following inequality:
y≥ 3 x +2
Solid line and shading above the line.