1. By: Andrea Bruno & William Wade

2. The BasicsPractice Problems Above & BeyondLinks For More Help and Games Just Click the Picture to go to that section Graphing Inequalities

3.  The basics of graphing Inequalities in two variables is graphing an open sentence that has:, ≤, or ≥. < : less than, dotted line on graph > : greater than, also a dotted line on graph ≤ : less than or equal to, solid line on graph ≥ : greater than or equal to, also a solid line on graph

4. Graphing Inequalities  The equation for graphing inequalities is y > mx + b b is the y-intercept and m is the slope of the line. The slope begins on the y-intercept Remember RISE over RUN Notice the dotted line! The 4 is the 1 st point on the y- intercept. The 2/1 is the slope going up 2 and over 1 Example 1

5. Shading  Part of solving inequalities is shading the solution  If the inequality is greater than or greater than or equal to you shade above the line  Less than or less than or equal to you shade below the line  The solution is where both shadings meet Example 2 1.After graphing the two inequalities you must shade (color) 2.Since the first (green) inequality is ≥ the line is solid and is shaded on top …with the other one the line is dotted and is also shaded on top

6. Converting Inequalities  Sometimes the inequality has a number with the y.  When this happens the problem must be converted back to slope intercept form ( y>mx+b ) : 2y>2x+4 Step 1: divide both sides by 2 (to get the y by itself) Step 2: write out the final equation (y>x+2) Step 3: Graph ~ 2 is the y intercept so put your first point on the y axis Step 3a: your slope is 1 or in fraction form 1/1 When multiplying or dividing with a negative number the sign of the inequality is flipped. For example: -y -x-9 in slope intercept form Notice the dotted line!! Back to Index Example 3

7. Practice Problems 1. 2y<8x-12y<8x-1 2. Y>-7x+5Y>-7x+5 3. 5y≤2x-3 & 2y>-5x+65y≤2x-3 & 2y>-5x+6 4. y≥-4x+8 & y<-5x+6y≥-4x+8 & y<-5x+6 5. -y<x-4 & y≥-x+7-y<x-4 & y≥-x+7 6. 17-x<y & 3y≤15x+117-x<y & 3y≤15x+1 7. -6+9x≥3y & 3y>-9x+6-6+9x≥3y & 3y>-9x+6 8. 9-3x≤y & 2y≥9x+39-3x≤y & 2y≥9x+3 9. -18+5x>-2y & y>8+5x-18+5x>-2y & y>8+5x 10. 1-10x<y & y≥3x-71-10x<y & y≥3x-7 Click the Equation to find out the Answers Back to Index

8.  Graphing advanced inequalities is no different from normal inequalities Just use 3 or more lines Create different polygons Also, find the area of those polygons If you don’t understand the Basic section, Do Not continue the Above & Beyond section The following inequalities were graphed: Y<4x -1 Y>-2.5x+3 Y≤0.5x -1 The Area where green, red, and blue are combined is the solution When you have 4 inequalities and is good enough to make a rectangle you can also find the area of that rectangle!! Back to Index

9. Links For More Help  http://www.glencoe.com/sec/math/algebra/alge bra1/algebra1_05/study_guide/pdfs/alg1_pssg_ G051.pdf http://www.glencoe.com/sec/math/algebra/alge bra1/algebra1_05/study_guide/pdfs/alg1_pssg_ G051.pdf  http://www.purplemath.com/modules/ineqgrph.h tm http://www.purplemath.com/modules/ineqgrph.h tm  http://www.math-play.com/Inequality- Game.html http://www.math-play.com/Inequality- Game.html  http://www.mathwarehouse.com/quadratic- inequality/how-to-solve-and-graph-quadratic- inequality.php http://www.mathwarehouse.com/quadratic- inequality/how-to-solve-and-graph-quadratic- inequality.php  http://www.sparknotes.com/math/algebra2/ineq ualities/section1.html http://www.sparknotes.com/math/algebra2/ineq ualities/section1.html Back to Index

10. Summary Tool ≤ Less Than or Equal to ≥ Greater than or equal to > Greater than < Less than When multiplying or dividing with a negative number the sign of the inequality is flipped The solution is where both shadings meet Remember RISE over RUN

11. Answer #1  4x-.5 is the simplified form of 2y<8x-1  Remember the dotted line  Also shaded below because the inequality is < Back to Index Back to Practice Problems

12. Answer #2  Remember the line is dotted  Also shaded above because the inequality is > Back to Index Back to Practice Problems

13. Answer #3  Watch the lines!  Shaded below on ≤ and above on > ≤ Back to Index Back to Practice Problems

14. Answer #4  Remember the line Back to Index Back to Practice Problems

15. Answer #5  Be sure to locate your solution Correctly Back to Index Back to Practice Problems

16. Answer #6 Back to Index Back to Practice Problems

17. Answer #7 Back to Index Back to Practice Problems

18. Answer #8 Back to Index Back to Practice Problems

19. Answer #9  Check your graphs  See the dotted lines! Back to Index Back to Practice ProblemsSorry about the graph but you should still know the area of the solution

20. Answer #10 Back to Index Back to Practice Problems  The inequalities are written in simplified form