Name Class Date. Graphing a Linear Inequality

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1 Name Class Date Solving Linear Inequalities Going Deeper Essential question: How do ou graph a linear inequalit in two variables? A linear inequalit in two variables, such as 2-6, results when ou replace the = sign in an equation b <, >,, or. A solution of an inequalit in two variables and is an ordered pair (, ) that makes the inequalit true. A-REI.4.2 EXAMPLE Graphing a Linear Inequalit Graph the solution set for 2-6. A Start b graphing 2 - = 6. The inequalit is true for ever point on this line because the inequalit smbol is less than or equal to. The line is called the boundar line of the solution set Houghton Mifflin Harcourt Publishing Compan B Test several other points in the plane that are not on the boundar line to determine whether the inequalit is true. Point Above or Below the Line? Inequalit True or False? (, ) Above 2() - () 6 False (, ) (, ) (4, 2) (6, ) The solutions of 2-6 lie on or 2 - = 6. Chapter 2 Lesson

2 C Shade the set of solutions to the inequalit 2-6. The shaded region and the boundar line make up the graph of 2-6. This area is referred to as a half-plane REFLECT a. How would the graph of 2-6 be like the graph of 2-6? How would it be different? b. Would the points on the boundar line 2 - = 6 be included in the graph of the inequalit 2 - > 6? Wh or wh not? c. Error Analsis A student sas that ou shade above the boundar line when the inequalit is > or and ou shade below it when the inequalit is < or. Use the eample to eplain wh this is not alwas true. To graph a linear inequalit in the coordinate plane:. Graph the boundar line. If the smbol is or, draw a solid line. If the smbol is < or >, draw a dashed line. Houghton Mifflin Harcourt Publishing Compan 2. Choose a test point (, ) that is not on the line. Substitute the values of and into the inequalit and determine whether it is true or false.. If the inequalit is true for the test point, shade the half-plane on the side of the boundar line that contains the test point. If not, shade the half-plane on the opposite side of the line. Chapter 28 Lesson

3 2 A-REI.4.2 EXAMPLE Graphing a Linear Inequalit in Two Variables Graph the inequalit - <. A Write the equation of the boundar line. B Graph the boundar line. The inequalit smbol is >, so the line will be dashed. C Test a point that is not on the line, such as (, ). ( ) - < True or false? Shade the part of the plane on the correct side of the line Houghton Mifflin Harcourt Publishing Compan REFLECT 2a. Wh is (, ) a good choice for a test point? When could ou not use (, )? 2b. For the graph of 4, the boundar line is the vertical line = 4. Would ou shade to the left or right of the boundar? Eplain. Chapter 2 Lesson

4 PRACTICE Graph the inequalit < Houghton Mifflin Harcourt Publishing Compan Chapter Lesson

5 . + 4 < Houghton Mifflin Harcourt Publishing Compan Chapter Lesson

6 > Houghton Mifflin Harcourt Publishing Compan Chapter 2 Lesson

7 Name Class Date Additional Practice. (, 6); < (, 2); 2. (, ); > <. Clark is having a part at his house. His father has allowed him to spend at most $2 on snack food. He d like to bu chips that cost $4 per bag, and pretzels that cost $2 per bag. a. Write an inequalit to describe the situation. Houghton Mifflin Harcourt Publishing Compan b. Graph the solutions. c. Give two possible combinations of bags of chips and pretzels that Clark can bu Chapter Lesson

8 Problem Solving Write the correct answer.. Shania would like to give $ gift cards and $4 tedd bears as part favors. Siteen people have been invited to the part. Shania has $ to spend on part favors. Write and graph an inequalit to find the number of gift cards and tedd bears Shania could purchase. 2. Hank has 2 ards of lumber that he can use to build a raised garden. Write and graph a linear inequalit that describes the possible lengths and widths of the garden. If Hank wants the dimensions to be whole numbers onl, what dimensions would produce the largest area? Select the best answer.. The roalties for the high school pla are $2. Tickets to the pla cost $ for students and $8 for nonstudents. What linear inequalit describes the number of student and nonstudent tickets that need to be sold so that the drama class can pa the roalties? A C + 8 < 2 B + 8 > 2 D A baker is making chocolate and lemon pound cakes. He can make at most 2 cakes at one time. Which inequalit describes the situation? A + > 2 C + 2 B + 2 D + < 2 4. The inequalit + 8 describes the amounts of two juices Annette combines to make a smoothie. Which is a solution to the inequalit? F (, 6) H (, 2) G (6, ) J (, ) 6. Erasmus is the master gardener for a universit. He wants to plant a miture of purple and ellow pansies at the west entrance to the campus. From past eperience, Erasmus knows that fewer than pansies will fit in the planting area. Which inequalit describes the situation? F + H + G + > J + < Houghton Mifflin Harcourt Publishing Compan Chapter 4 Lesson