1. 2-8: Graphing Inequalities in the Coordinate Plane Algebra 2 CP

2. Graphing Inequalities in the Coordinate Plane When a line is drawn in a plane, the line separates the plane into __________ distinct regions called ________________. The line itself is the ________________ of the two regions. The boundary does __________ belong in either half plane. half-planes two boundary not half-plane

3. Example 1: Graph y > 2x + 7 When graphing an inequality, follow these steps: 1. Graph the boundary line – either dashed or solid. 2. Select a point (not on the line) from each half plane. 3. Shade the half plane that satisfies the equation or plot points if it is a discrete situation. Test (0, 0) y > 2x + 7 0 > 0 + 7 Test (-4, 0) y > 2x + 7 0 > -8 + 7 0 > -1

4. Example 2: Graph y  -3x - 2 When graphing an inequality, follow these steps: 1. Graph the boundary line – either dashed or solid. 2. Select a point (not on the line) from each half plane. 3. Shade the half plane that satisfies the equation or plot points if it is a discrete situation. Test (0, 0) y ≤ -3x - 2 0 ≤ 0 - 2 Test (-4, 0) y ≤ -3x - 2 0 ≤ 12 - 2 0 ≤ 10 0 ≤ - 2

5. Example 3: You put up a new shelf that is 1 ft. wide to store some of your books and trophies. Each book takes up 1 in. and each trophy takes up 3 in. what is a graph showing how many books and how many trophies will fit on the shelf? Relate # of Books# of Trophies Define B = # of BooksT = # of Trophies Write Find the intercepts of the boundary line and graph the boundary line. Trophies Books

6. Trophies Books This is a __________________ so the shaded region really represents all the points for the ___________________ possibilities. Discrete Graph Whole Number Because you can’t have half a book or trophy.

7. Graphing an Absolute Value Inequality When graphing an Absolute Value inequality, follow these steps: 1. Solve the inequality for y 2. Graph the boundary line – either dashed or solid. 3. Select a point (not on the line) from each half plane. 4. Shade the solution Test (0, 0)Test (0, 4)

8. What Inequality Does This Graph Represent? 1. How is the vertex translated?From (0, 0) to (2, 1) 2. Is the solution above or below the boundary line? It is above so the inequality is either > or ≥. 3. Is the boundary line dashed or solid? It is dashed so the inequality is >.

9. Homework: p. 118 #9, 11, 15-21 odd, 31, 33, 40-44 even, 56-70 even