Lesson 6 6 Graphing Inequalities in Two Variables

Lesson 6 -6 Graphing Inequalities in Two Variables

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Objectives • Graph inequalities on the coordinate plane • Solve real-world problems involving linear inequalities

Vocabulary • Half-plane – the region of the graph of an inequality on one side of a boundary • Boundary – a line or curve that separates the coordinate plane into regions

Four Step Problem Solving Plan • Step 1: Explore the Problem – Identify what information is given (the facts) – Identify what you are asked to find (the question) • Step 2: Plan the Solution – Find an equation the represents the problem – Let a variable represent what you are looking for • Step 3: Solve the Problem – Plug into your equation and solve for the variable • Step 4: Examine the Solution – Does your answer make sense? – Does it fit the facts in the problem?

Example 1 From the set {(3, 3), (0, 2), (2, 4), (1, 0)}, which ordered pairs are part of the solution set for Use a table to substitute the x and y values of each ordered pair into the inequality. x y True or False 3 3 true 0 2 false 2 4 true 1 0 false

Example 1 cont Answer: The ordered pairs {(3, 3), (2, 4)} are part of the solution set of. In the graph, notice the location of the two ordered pairs that are solutions for in relation to the line.

Example 2 Step 1 Solve for y in terms of x. Original inequality Add 4 x to each side. Simplify. Divide each side by 2. Simplify.

Example 2 cont Step 2 Graph Since does not include values when the boundary is not included in the solution set. The boundary should be drawn as a dashed line. y = 2 x + 3 Step 3 Select a point in one of the half-planes and test it. Let’s use (0, 0). Original inequality false Answer: Since the statement is false, the half-plane containing the origin is not part of the solution. Shade the other half-plane.

Example 3 Journalism Lee Cooper writes and edits short articles for a local newspaper. It generally takes her an hour to write an article and about a half-hour to edit an article. If Lee works up to 8 hours a day, how many articles can she write and edit in one day? Step 1 Let x equal the number of articles Lee can write. Let y equal the number of articles that Lee can edit. Write an open sentence representing the situation. Number of articles she can write plus x + hour times number of articles she can edit is up to 8 hours. y 8

Example 3 cont Step 2 Solve for y in terms of x. Original inequality Subtract x from each side. Simplify. Multiply each side by 2. Simplify.

Example 3 cont Step 3 Since the open sentence includes the equation, graph as a solid line. Test a point in one of the half-planes, for example, (0, 0). Shade the half-plane containing (0, 0) since is true. Answer:

Summary & Homework • Summary: – To graph an inequality in two variables • Step 1: Determine the boundary and draw a dashed or solid line • Step 2: Select a test point. Test that point. • Step 3: Shade the half-plane that contains the solution • Homework: – pg 356 12 -36 even