6.7 Graph Linear Inequalities in Two Variables
Learning Target
We learned how to graph linear equations in
two variables. Now we will graph linear
inequalities in two variables. We will use our
knowledge of graphing a line, then shade one
side of the line where the solutions of the
linear inequality lie. You will have mastered
this learning target when you can use this
knowledge to solve an application problem.
Jan 24­8:30 PM
P.O.D.
Is (2, -1) a solution of x + 2y = 4?
Jan 24­8:40 PM
P.O.D.
y
Graph x - 3y = 6
6
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Jan 24­8:42 PM
1
A linear inequality in two variables such as
x - 3y < 6 is the result of replacing the = sign
in a linear equation with an inequality sign.
A solution of an inequality in two variables
x and y is an ordered pair that produces a
true statement when the values of x and y
are substituted into the inequality.
Jan 24­8:44 PM
Keystone test practice
Which ordered pair is not a solution of
x - 3y < 6?
A. (0, 0) B. (6, -1) C. (10, 3) D. (-1, 2)
Jan 24­8:49 PM
Which ordered pair is a solution of
-x + 2y < 8?
1. (0,0)
2. (0, 4)
3. (3, 5)
Jan 24­8:55 PM
2
Key Concept
Graphing a Linear Inequality in two Variables
Step 1:Graph the line, called a boundary line. Use a dashed line for < or >, and use a solid line for or
Step 2:Test a point not on the boundary line by checking whether the ordered pair is a solution of the inequality.
Step 3:Shade the half­plane containing the point if the ordered pair is a solution of the inequality. Shade the other half­plane if the ordered pair is not a solution.
Jan 24­8:58 PM
Example Graph a linear inequality in two variables
Graph the inequality y > 4x ­ 3
y
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1
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x
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Jan 24­9:08 PM
Graph the inequality x + 2y y
6
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0
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Jan 24­9:11 PM
3
Guided Practice
Graph x + 3y > ­1
y
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Jan 24­9:14 PM
Linear Inequalities in one variable
The boundary line for a linear inequality in one variable is either a vertical or horizontal line.
• If an inequality has only the x variable, substitute the x coordinate of the test point into the inequality.
• If an inequality has only the y variable, substitute the y coordinate of the test point into the inequality.
Jan 24­9:15 PM
Graph the inequality y y
6
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0
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Jan 24­9:21 PM
4
Graph the inequality x < ­1
y
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Jan 24­9:22 PM
Guided Practice
Graph the inequality
y
6
5
4
1. y > 1
3
2
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0
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Jan 24­9:24 PM
2. y y
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Jan 24­9:26 PM
5
y
3. x < ­2
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Jan 24­9:27 PM
Application Problem
You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour teaching swimming. Let x represent the number of hours you teach basketball each week, and y represent the number of hours you teach swimming each week. Your goal is to earn at least $200 per week.
• Write an inequality that describes your goal in terms of x and y.
• Graph the inequality.
• Give three possible combinations of hours thst will allow you to meet your Jan 24­9:29 PM
Closure
Graph the inequality 2x ­ 6y > ­36
y
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2
1
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0
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x
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Jan 24­9:37 PM
6