Post on 18-Jan-2018
description
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Math 51
3.5Graphing Linear Inequalities in Two
Variables
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Solutions to the linear equation are points on the line shown below:
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Solutions to the linear inequality include all the points on and above the line:
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Note: the line would be called the boundary line for .
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1. Solve the inequality for .
2. Graph the boundary line. Use __________________ if have or . Use __________________ if have or .
3. If you have “” or “”, then shade half-plane _____________ the line.
If you have “” or “”, then shade half-plane _____________ the line.
How to Graph Linear Inequalities in Two Variables
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1. Solve the inequality for .
2. Graph the boundary line. Use __________________ if have or . Use __________________ if have or .
3. If you have “” or “”, then shade half-plane _____________ the line.
If you have “” or “”, then shade half-plane _____________ the line.
How to Graph Linear Inequalities in Two Variables
dashed line
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1. Solve the inequality for .
2. Graph the boundary line. Use __________________ if have or . Use __________________ if have or .
3. If you have “” or “”, then shade half-plane _____________ the line.
If you have “” or “”, then shade half-plane _____________ the line.
How to Graph Linear Inequalities in Two Variables
dashed linesolid line
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1. Solve the inequality for .
2. Graph the boundary line. Use __________________ if have or . Use __________________ if have or .
3. If you have “” or “”, then shade half-plane _____________ the line.
If you have “” or “”, then shade half-plane _____________ the line.
How to Graph Linear Inequalities in Two Variables
dashed linesolid line
above
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1. Solve the inequality for .
2. Graph the boundary line. Use __________________ if have or . Use __________________ if have or .
3. If you have “” or “”, then shade half-plane _____________ the line.
If you have “” or “”, then shade half-plane _____________ the line.
How to Graph Linear Inequalities in Two Variables
dashed linesolid line
above
below
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1. Solve the inequality for .
2. Graph the boundary line. Use __________________ if have or . Use __________________ if have or .
3. If you have “” or “”, then shade half-plane _____________ the line.
If you have “” or “”, then shade half-plane _____________ the line.
How to Graph Linear Inequalities in Two Variables
dashed linesolid line
above
below
(See http://www.geogebratube.org/student/m6368 to understand why above/below.)
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Ex 1.Graph: .
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Ex 1.Graph: .
𝑦 ≤ 32 𝑥−3
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Ex 1.Graph: .
𝑦 ≤ 32 𝑥−3
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Ex 1.Graph: .
𝑦 ≤ 32 𝑥−3
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Ex 1.Graph: .
𝑦 ≤ 32 𝑥−3
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Ex 1.Graph: .
𝑦 ≤ 32 𝑥−3
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Ex 2.Graph: .
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Ex 2.Graph: .
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Ex 2.Graph: .
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Ex 2.Graph: .
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Ex 2.Graph: .
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Ex 3.Graph: .
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Ex 3.Graph: .
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Ex 3.Graph: .
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Ex 4.Graph: .
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Ex 4.Graph: .
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Ex 4.Graph: .