1. A LGEBRA I G RAPHING I NEQUALITIES IN THE P LANE Small Group Lesson Notes Week of May 18, 2009

2. G RAPHING L INEAR I NEQUALITIES IN THE P LANE There are TWO important things to remember when graphing inequalities in a plane: 1. What TYPE of line to graph and 2. WHERE TO SHADE The following slides will help you learn and remember these two important aspects of graphing inequalities in a plane…

3. (C ONTINUED …) G RAPHING L INEAR I NEQUALITIES IN THE P LANE Graphing Inequalities is similar to graphing lines using the y = mx + b (slope-intercept) form of the line First, graph the y-intercept and then use the slope from the equation to determine “how many up/down and how many over” you need to go to place the second point. When graphing an inequality you must sometimes connect the dots with a dotted line instead of a solid line. The next slide will help you determine what kind of line you should draw…

4. (C ONTINUED …) G RAPHING L INEAR I NEQUALITIES IN THE P LANE If the inequality symbol is, draw the boundary as a dashed line. If the inequality symbol is or, draw the boundary as a solid line to show that the points on the boundary are included in the solution set. What TYPE of line….dotted line or solid line???

5. (C ONTINUED …) G RAPHING L INEAR I NEQUALITIES IN THE P LANE After deciding whether to draw a dotted line or a solid line, you must determine which SIDE of the line to shade. If the equation is in slope-intercept form and reads “y is greater than” or “y is greater than or equal to,” then you’ll graph ABOVE the line. If the equation is in slope-intercept form and reads “y is less than” or “y is less than or equal to,” then you’ll graph BELOW the line. The next slide will help you visualize this concept…

6. (C ONTINUED …) G RAPHING L INEAR I NEQUALITIES IN THE P LANE y is greater than 2x-1y is less than or equal to x+3 …means “shade above the line”…means “shade below the line” WHERE TO SHADE….above or below the line???

7. (C ONTINUED …) G RAPHING L INEAR I NEQUALITIES IN THE P LANE Choose the correct graph. Answer and explanation on next slide…

8. (C ONTINUED …) G RAPHING L INEAR I NEQUALITIES IN THE P LANE “ greater than or equal to” means solid line and shade above the line.

9. (C ONTINUED …) G RAPHING L INEAR I NEQUALITIES IN THE P LANE Choose the correct graph. Answer and explanation on next slide…

10. (C ONTINUED …) G RAPHING L INEAR I NEQUALITIES IN THE P LANE “ less than ” means dotted line and shade below the line.

11. (C ONTINUED …) G RAPHING L INEAR I NEQUALITIES IN THE P LANE Overall, there are TWO important things to remember when graphing inequalities in a plane: 1. What TYPE of line to graph (dotted or solid) and 2. WHERE TO SHADE (above or below the line) If you remember these two things, you should be successful at graphing inequalities in a plane!