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Graphing Inequalities on the Coordinate Plane

Learn how to graph inequalities on the coordinate plane and solve real-world problems involving linear inequalities in this lesson.

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Graphing Inequalities on the Coordinate Plane

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  1. Lesson 6-6 Graphing Inequalities in Two Variables

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

  3. Transparency 6a

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

  5. 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

  6. 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?

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

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

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

  10. 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. Original inequality false Example 2 cont y = 2x + 3 Step 3 Select a point in one of the half-planes and test it.Let’s use (0, 0). Answer: Since the statement is false, the half-plane containing the origin is not part of the solution. Shade the other half-plane.

  11. Number of articlesshe can write plus hour times number of articlesshe can edit is up to 8 hours. x + y 8 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.

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

  13. Step 3 Since the opensentence includes the equation, graph asa solid line. Test a point in one of the half-planes, for example, (0, 0). Shade the half-plane containing (0, 0) since istrue. Example 3 cont Answer:

  14. 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

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