Understanding Linear Inequalities in Two Variables
Explore the concept of linear inequalities in two variables through graphing and modeling real-world situations. Learn how to identify solutions, graph inequalities, and determine shading direction. Practice problems and visual examples enhance understanding of these mathematical concepts.
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Presentation Transcript
6-5 Linear Inequalities Learning Target: 1) I can graph linear inequalities in two variables 2) I can use linear inequalities when modeling real-world situations
Linear Inequality: in two variables, such as ? > ? 3can be formed by replacing the equal sign in a linear equation with an inequality symbol Solution of an inequality: in two variable is an ordered pair that makes the inequality true.
Problem 1: Identifying Solutions of a Linear Inequality Is the ordered pair a solution of ? > ? 3 (1,2)
What you need to know: Type of Lined needed: < or > Dashed line ?? Solid Line Where to Shade: ? > or y Shade Above ? < or y Shade Below
Problem 2: Graphing an Inequality in Two Variables What is the graph of ? > ? 2
What is the graph of ? 1 2? + 1
Problem 3: Graphing a Linear Inequality in One Variable What is the graph of ? > 1
Problem 4: Rewriting to Graph an Inequality An interior decorator is going to remodel a kitchen. The wall above the stove and the counter is going to be redone as shown. The owners can spend $420 or less. Write a linear inequality and graph the solutions. What are 3 possible prices for the wallpaper and tiles?
For a party, you can spend no more than $12 on nuts. Peanuts cost $2/lb. Cashews cost $4/lb. What are three possible combinations of peanuts and cashews you can buy?
Problem 5: Writing an Inequality From a Graph What is the inequality that represents the graph?
