4.5 Linear Inequalities in Two Variables What are your objectives for Section 4.5? How can you accomplish each objective? 1 Define a Linear Inequality in Two Variables • Understand the defi nition of a linear inequality in two variables, and write it in your notes. • Complete the given example on your own. • Complete You Try 1. 2 Graph a Linear Inequality in Two Variables • Understand the defi nitions of a half plane, boundary line, and test point. • Learn the procedure for Graphing a Linear Inequality in Two Variables Using the Test Point Method, and write it in your notes. • Learn the procedure for Using Slope-Intercept Form to Graph a Linear Inequality in Two Variables, and write it in your notes. • Complete the given examples on your own. • Complete You Trys 2 and 3. 3 Solve a System of Linear Inequalities by • Learn the procedure for Solving a System of Linear Inequalities by Graphing, and write it in your notes. • Complete the given examples on your own. • Complete You Trys 4–6. Read the explanations, follow the examples, take notes, and complete the You Trys. In Chapter 2, we fi rst learned how to solve linear inequalities in one variable such as 4x 9 7. In this section, we will fi rst learn how to graph the solution set of a linear inequality in two variables. Then we will learn how to graph the solution set of systems of linear inequalities in two variables. 1 Define a Linear Inequality in Two Variables Graphing Definition A linear inequality in two variables is an inequality that can be written in the form Ax By C or Ax By C, where A, B, and C are real numbers and where A and B are not both zero. ( and may be substituted for and .) Here are some examples of linear inequalities in two variables. 2x 5y 3, y 1 5 x 2, x 6, y 1 Note x 6 can be considered a linear inequality in two variables because it can be written as x 0y 6. Likewise, y 1 can be written as 0x y 1. 286 CHAPTER 4 Linear Equations and Inequalities in Two Variables www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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