Graphing Linear Inequalities in Two Variables Section 2

Graphing Linear Inequalities in Two Variables Section 2. 8

Review Which of the following ordered pairs is a solution of 2 x + 5 y > 9? A) B) C) D) 7/20/2012 9: 41 PM (– 4, – 1) (– 2, 3) (2, – 4) (6, – 1) 2. 8: Graph Linear Inequalities in Two Variables 2

Steps in Graphing A. Draw the graph either applying slope–intercept or quick graph form 1. When using “cover–up, ” if there is a negative coefficient in the y, flip the direction of the graph B. Determine what the sign is and graph the line 1. Dotted Line: Greater, Less, or not–equal to 2. Solid Line: Greater then OR equal to, Less than OR equal to, Equal to C. Shade above or below the line by looking at inequality 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 3

Steps in Graphing Greater Than 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 4

Steps in Graphing Less Than 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 5

Example 1 Graph 2 x + 3 y < 6 Graph, as if, it was an equality. OR (3, 0) and (0, 2) 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 6

Example 2 Graph – 4 x – 2 y > 8 OR (– 2, 0) and (0, – 4) 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 7

Example 2 Calculator Graph – 4 x – 2 y > 8 Must be in slope–intercept form Go to Y= in graphing calculator Greater than Less than 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 8

Example 2 Calculator Graph – 4 x – 2 y > 8 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 9

Example 3 Graph y > 4 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 10

Example 4 Graph x < 7 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 11

Your Turn Graph 3 > 3/2 y y<2 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 12

Example 5 Graph 2/3 (2 x – y) < 2 y > 2 x – 3 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 13

Example 6 $12 an hour job (every 5) You have two part–time summer jobs, one that pays $9 and hour and another that pays $12 an hour. You would like to earn at least $240 a week. Write an inequality describing the possible amounts of times you can schedule at each jobs. Graph the inequality. Each space is worth 5. 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables $9 an hour job (every 5) 14

Your Turn Large Pizzas (per 50) A pizza place has 4800 ounces (300 pounds) of dough. A small pizza uses 12 ounces of dough and a large pizza uses 18 ounces of dough. Write and graph an inequality describing the possible numbers of small and large pizzas that can be made. Each space is worth 50. 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables Small Pizzas (per 50) 15

Assignment Page 135 3– 27 odd, 43– 47 odd 7/20/2012 9: 41 PM 2. 8: Graph Linear Inequalities in Two Variables 16