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Graph Linear InequalitiesTeacher Notes

Graph Linear InequalitiesTeacher Notes

Here is our procedure for graphing linear inequalities.• Step 1 – Graph line• Step 2 – Draw the line• Step 3 – Test points not on the line• Step 4 – Shade the solution half-plane.

IQ.3 Graph Linear InequalitiesIQ.3 Graph Linear Inequalities

Graphs on the Half-Plane

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A-REIc I can represent and solve equations and inequalities graphically.

Graph linear inequalities or systems of inequalities by hand or with technology.

Graph the one-variable inequality.• 5 – 3x > -7

• 5 – 3x ≤ -7

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LaunchLaunch

Types of InequalitiesTypes of Inequalities

What are the types of inequalities?

• >

• <

• ≥

• ≤

How do they look on coordinate grid?

Graph y ≤ 3x + 2 Graph y ≤ 3x + 2 • Step 1: Graph y = 3x + 2 – y-intercept– slope

Graph y ≤ 3x + 2 Graph y ≤ 3x + 2 • Step 1: Graph y = 3x + 2 – y-intercept– Slope

• Step 2: Draw line

Graph y ≤ 3x + 2 Graph y ≤ 3x + 2 • Step 3: Test a

point not on the line.

• Let’s test (-2, -2)(-2) ≤ 3(-2) + 2-2 ≤ -6 + 2 -2 ≤ -4FALSE

So, (-2, -2) is not a solution to the inequality.

So, (-2, -2) is not a solution to the inequality.

Graph y ≤ 3x + 2 Graph y ≤ 3x + 2 • Step 3: Test a

point on the other side of line.

• Let’s test (1, 1)(1) ≤ 3(1) + 21 ≤ 3 + 2 1 ≤ 5TRUE So, (1, 1) is a solution

to the inequality.So, (1, 1) is a solution

to the inequality.

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So, (1, -1) is a solution to the inequality.

So, (1, -1) is a solution to the inequality.

Graph y ≤ 3x + 2 Graph y ≤ 3x + 2 • Step 4: Shade

the solution half-plane.

The side of the line with (1, 1) is the solution to the inequality, so shade that side of the line.

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DebriefDebriefWhat is a dotted line used when

graphing a linear inequality on a graph similar to when graphing a one-variable inequality on a number line?

How many points do you need to test to decide which side of a line to graph on an inequality? What are good points to test? Support your answer.

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Ticket Out

This is the graph of y < 3x + 2

• Which of these points are a solution?

• Show work to support whether or not the points are a solution.

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Ticket Out

This is the graph of y < 3x + 2

• Which of these points are a solution?

• Show work to support whether or not the points are a solution.

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Ticket Out

This is the graph of y < 3x + 2

• Which of these points are a solution?

• Show work to support whether or not the points are a solution.

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Ticket Out

This is the graph of y < 3x + 2

• Which of these points are a solution?

• Show work to support whether or not the points are a solution.