Lesson 6-6 Graphing Inequalities in Two Variables

Transparency 6 Click the mouse button or press the Space Bar to display the answers.

Transparency 6a

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. false 01 true 42 false 20 true 33 True or False yx

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 forin relation to the line.

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

Example 2 cont Step 2 Graph Sincedoes not include values when the boundary is not included in the solution set. The boundary should be drawn as a dashed line. 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. y = 2x + 3

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 writeplustimes number of articles she can editis up to8 hours. hour x+8y

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 even