LOG 4 Lesson D: Linear Inequalities in Two Variables

​Linear Inequalities in Two Variables

Day 1 Objective: Determine if an ordered pair is a solution of a linear inequality in two variables (equation and graph).​

State Standard: ​A1.AREI.12

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1) Linear inequality -

a linear equation that replaces the equal sign with an inequality symbol.​

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​Students should write important vocabulary and examples in their notes/binder.

​Important Vocabulary

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2) Solution of a linear inequality -

an ordered pair, (x, y), that makes the inequality true.

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​Students should write important vocabulary and examples in their notes/binder.

​Important Vocabulary

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3) Half plane -

a region of the coordinate plane that is either shaded above or below the graphed line.

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​Students should write important vocabulary and examples in their notes/binder.

​Important Vocabulary

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​Example #1

1) Substitute the x- and y-values into the inequality given.

2) Evaluate both sides of the inequality.

3) Determine if the statement is true.​

​To determine if an ordered pair is a solution of a linear inequality, you must:

​Solutions of a Linear Inequality - Equation

Students should write important vocabulary and examples in their notes/binder.

​Example #2

1) Substitute the x- and y-values into the inequality given.

2) Evaluate both sides of the inequality.

3) Determine if the statement is true.​

​To determine if an ordered pair is a solution of a linear inequality, you must:

​Solutions of a Linear Inequality - Equation

Students should write important vocabulary and examples in their notes/binder.

​Now you try!

​Please use your notes to ensure mastery of the standard.

Multiple Choice

Determine if (-1, 2) is a solution to the inequality, $$y<-x+2$$ .

• Yes, (-1, 2) is a solution.

• No, (-1, 2) is not a solution.

​Worked

Solution

Multiple Choice

Determine if (-1, 2) is a solution to the inequality, $$3x+4y<5$$ .

• Yes, (-1, 2) is a solution.

• No, (-1, 2) is not a solution.

​Worked

Solution

​Example #1

1) Located in the shaded area or

2) Located on a solid line (not dashed line).

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​To determine if an ordered pair is a solution of a graphed linear inequality, the ordered pair must be:

​Solutions of a Linear Inequality - Graph

Students should write important vocabulary and examples in their notes/binder.

​Which ordered pair is a solution to the inequality?

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Answer: B and D

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A is not because the line is dashed.​

​Homework

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(Extra Practice #1) LOG 4 Lesson D in Edulastic​

LOG 4 Lesson D in Edulastic​​

​Please use your notes to ensure mastery of the standard.

Poll

Do you have any questions?

• I understand the lesson and do not have any questions.

• I need help on solutions of an inequality.

• I need help with solutions of a graphed inequality.

• I need help with both solutions.