1. 8.3 Linear Inequalities in Two Variables BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 4.The next step is to determine which side of the line to shade. Pick any ordered pair that is not on the graphed line. This will be your test point. Substitute the coordinates of that ordered pair into the original inequality. If the inequality is true, shade the side of the line where the test point is. If the inequality is false, shade the other side of the line. Any coordinate in the shaded region will be true in the inequality. Any coordinate in the region not shaded will be false in the inequality. 2. Find three points on the line. Let x = 0, solve for y. Let y = 0, solve for x. Choose a 3 rd value for x (not zero or the x-intercept). 3. Draw the line. If the inequality symbol is  or , draw a solid line. If the inequality symbol is > or <, draw a dashed line. Procedure for Graphing Linear Inequalities using the Intercept Method 1. Rewrite the linear inequality as a linear equation. (i.e., change the inequality symbol to an equal sign.) Linear Inequalities in two variables are of the form Ax + By > C, Ax +By < C, Ax + By  C or Ax + By  C where A,B, and C are real numbers. Examples of linear inequalities in two variables: 4x + 2y > 12, x – y < 1, y  2x – 3, 2x – 3y  6

2. 8.3 Linear Inequalities in Two Variables BobsMathClass.Com Copyright © 2010 All Rights Reserved. 2 Step 1. Write the inequality as an equation. Step 2. Find 3 points. Step 3. Since the inequality symbol is , draw a solid line. Step 4. Pick a test point not on the line to determine which point to shade. Next Slide x y Let x=0, solve for y. Then let y=0, solve for x. 0 0 2 3 Now we need a third point. Choose any value for x except 0 and 2. Let’s choose x=4. 4 -3 Test Point: Since this is true, shade the side of the test point.

3. 8.3 Linear Inequalities in Two Variables BobsMathClass.Com Copyright © 2010 All Rights Reserved. 3 Your Turn Problem #1 x y 0 7 3 -2 0 -1 1/7

4. 8.3 Linear Inequalities in Two Variables BobsMathClass.Com Copyright © 2010 All Rights Reserved. 4 Graphing Inequalities involving Vertical and Horizontal Lines Recall: The graph of an equation y=k, where k is any real number, is a horizontal line. The graph of an equation x=c, where c is any real number, is a vertical line. 1. Graph the line y=2. y=# is a horizontal line. Since the inequality is <, draw a dashed line. 2. Choose a test point. Next Slide Then use a test point to determine which side to shade. (0,0) (0,0) is usually chosen because the math will be easier. The only time we can not choose (0,0) is if the line goes through (0,0), the origin. Therefore, shade the side that does not have the test point.

5. 8.3 Linear Inequalities in Two Variables BobsMathClass.Com Copyright © 2010 All Rights Reserved. 5 Your Turn Problem #2

6. 8.3 Linear Inequalities in Two Variables BobsMathClass.Com Copyright © 2010 All Rights Reserved. 6 2. Graph the line x=-2. x=# is a vertical line. Since the inequality is >, draw a dashed line. 3. Choose a test point to determine which side to shade. Next Slide 1. Simplify the inequality. -2 (Don’t forget, if you multiply or divide by a negative #, invert the inequality symbol)

7. 8.3 Linear Inequalities in Two Variables BobsMathClass.Com Copyright © 2010 All Rights Reserved. 7 Your Turn Problem #3

8. 8.3 Linear Inequalities in Two Variables BobsMathClass.Com Copyright © 2010 All Rights Reserved. 8 Graphing Compound Inequalities in Two Variables The solution to a system of inequalities are all the points which satisfy each of the inequalities. Recall that the word “and” indicates the intersection of the solutions sets of each inequality. 1. Graph each inequality and shade the correct region lightly. 2. The region which is shaded for each inequality is the desired region. Procedure for Graphing a System of Inequalities: 1. Graph x  -2. 2. Graph y < -1. 3. The area that is shaded twice is our desired region. Next Slide

9. 8.3 Linear Inequalities in Two Variables BobsMathClass.Com Copyright © 2010 All Rights Reserved. 9 Your Turn Problem #4 The End B.R. 11-20-06