This document discusses how to graph linear inequalities on a coordinate plane. It explains that less than and greater than signs are represented by dashed lines, while less than or equal to and greater than or equal to signs use solid lines. It notes that inequalities must be written in slope-intercept form before graphing and that the shading depends on whether the inequality involves less than or greater than. Specifically, y greater than inequalities are shaded above the line and y less than inequalities are shaded below the line. Practice graphing many problems to fully understand how to determine the shading direction.

1. Linear Inequalities

2. Background How do you graph x < 1 on the number line?

3. Background On the coordinate plane, x < 1 is graphed like this:

4. Background For inequalities on the coordinate plane: < & > are represented with a dashed line ≤ & ≥ are represented with a solid line (non-dashed line)

5. x without y x > # x ≤ #

6. y without x y > # y ≤ #

7. Linear Inequalities Make sure the inequality is in slope intercept form. All the rules you know about inequalities apply here: If you multiply or divide by a negative number you have to flip the sign.

8. Linear Inequalities After the equation is in slope intercept form, graph the line. Use a dashed line if the sign is < or >. The big thing is, understanding where to shade. The sign helps you know where to shade.

9. Linear Inequalities y > will be shaded toward the top of the graph

10. Linear Inequalities y < will be shaded toward the bottom of the graph

11. Linear Inequalities y < will be shaded toward the bottom of the graph

12. Linear Inequalities Since every graph lays on the coordinate plane differently, toward the top and toward the bottom is a bit subjective. The best way to get a good feel for it is to work a lot of problems.