math 51 3.5 graphing linear inequalities in two variables 1
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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
![Page 8: Math 51 3.5 Graphing Linear Inequalities in Two Variables 1](https://reader036.vdocument.in/reader036/viewer/2022062504/5a4d1b287f8b9ab059997e37/html5/thumbnails/8.jpg)
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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: .