Graphing Inequalities in Two Variables

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
Example 1
Use a table to substitute the x and y values of
each ordered pair into the inequality.
8
Example 1 cont
9
Example 2
Step 1 Solve for y in terms of x.
10
Example 2 cont
y 2x 3
Step 3 Select a point in one of the half-planes
and test it.Lets 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
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
Example 3 cont
Step 2 Solve for y in terms of x.
13
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