Graph. y ≥-3 x ≥1

Name: Problem 40, Chapter 4: Intermediate Algebra : Concepts and Applications
Uploaded: 2020-07-13T14:34:14-08:00
Duration: 1 min 26 s
Channel: Ankit Gupta
Description: Graph. y ≥-3 x ≥1

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Key Concepts

Graphing Linear Inequalities

Graphing linear inequalities involves plotting the boundary line that corresponds to the equality version of the inequality (for example, y = -3 or x = 1) and then shading the region of the plane that satisfies the inequality. A solid line is used if the inequality includes equality (? or ?), while a dashed line indicates that the boundary itself is not part of the solution.

Half-planes

Every linear inequality partitions the Cartesian plane into two regions, known as half-planes. One half-plane contains all the points that satisfy the inequality, while the other contains points that do not. Identifying which half-plane to shade can often be done by testing a specific point that is not on the boundary line.

Feasible Region

When multiple inequalities are given, the feasible region is the intersection of all the individual half-planes. This region represents all the solutions that simultaneously satisfy all the inequalities. Understanding how to determine and graph the feasible region is crucial for solving problems in areas such as linear programming and optimization.

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