1. Chapter 3 Section 3.7 Graphing Linear Inequalities

2. Graphing a Linear Inequality Some examples of linear inequalities are seen to the right. They all use the symbols of either,. Their graphs are always one half of the plane either the above or below a line or left or right of a line. The line is either solid or dashed. The graphs represent the points that are solutions to the inequality. Graphing Inequalities that have only one variable means you are looking at a region that has either a vertical (if only x is used) or horizontal (if only y is used) boundary. x < 3 x = 3 x > -4 x = -4 y > 1 y = 1 y < -3 y = -3 -6-5-4-3-2123456 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6-5-4-3-2123456 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6-5-4-3-2123456 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6-5-4-3-2123456 -6 -5 -4 -3 -2 1 2 3 4 5 6

3. Graphing Linear Inequalities To graph a linear inequality that involves both x and y we do the following: 1.Solve the inequality for y. (Important if you need to multiply or divide by a negative you need to reverse the direction the inequality points!) 2.Treat it as if it were a line graphing it with either a solid or dashed line. 3.If it is > or > shade above the line. If it is < or < shade below the line. Graph: 4 x – 2 y < 6 Solve Divide by -2. Reverse. y = 2 x - 3 Graph: y < -3 x + 6 This inequality is already solved for y. We do not need to do this step. y = -3 x + 6 Shade what is above the line. Shade what is Below the line. -6-5-4-3-2123456 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6-5-4-3-2123456 -6 -5 -4 -3 -2 1 2 3 4 5 6