Graphing Linear Inequalities on a Grid

MATH 017

Intermediate Algebra

S. Rook

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Overview

• Section 3.6 (Objective 1) in the textbook– Graphing Linear Inequalities including finding

test points and shading

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Graphing Linear Inequalities

• We know 3 ways to graph:– Table of Values– Intercepts– By slope and y-intercept

• No different than graphing linear equalities except for:– Whether the line is solid (≤, ≥) or broken

(<, >)– Shading one side of the line

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Test Points and Shading

• After constructing the line, pick a test point that does NOT lie on the line– (0, 0) is often a good choice

• Substitute the x and y values into the inequality and simplify– If the statement is true, shade the side WITH

the test point– If the statement is false, shade the side

WITHOUT the test point

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Graphing Linear Inequalities on a Grid (Example)

Ex 1: Graph y ≥ -3x – 1

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Graphing Linear Inequalities on a Grid (Example)

Ex 2: Graph 5x – 3y < 12

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Graphing Linear Inequalities on a Grid (Example)

Ex 3: Graph x ≤ 2y

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Graphing Linear Inequalities on a Grid (Example)

Ex 4: Graph 1

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3

2 y

x

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Summary

• After studying these slides, you should know how to do the following:– Graph a linear inequality on a coordinate grid

and correctly shade one side of the line based on a test point