Graph the inequality x-y ≥3. How do you know which side of the line x-y=3 should be shaded?

Name: Problem 325, Chapter 5: Elementary Algebra
Uploaded: 2021-08-05T21:51:25-08:00
Duration: 2 min 35 s
Channel: Destin Priester
Description: Graph the inequality x-y ≥3. How do you know which side of the line x-y=3 should be shaded?

step 1 Okay, you have x minus y is greater than equal to three. So you're going to grab him, and I like

Graph the inequality x-y ≥3. How do you know which side of...

Key Concepts

Linear Inequalities

Linear inequalities are mathematical expressions that involve a linear function with an inequality sign (such as >, ?, <, or ?) instead of an equality. They represent a range of solutions on the coordinate plane, and the goal is to determine all the points that satisfy the inequality. This concept is crucial when graphing because it demonstrates how the algebraic relationship defines a region rather than a single line.

Boundary Lines

The boundary line in the context of a linear inequality is the line that results from replacing the inequality sign with an equality. This line divides the plane into two regions and serves as a reference for determining which side of the line represents the solution set of the inequality. It is drawn as a solid line if the inequality includes equality (? or ?) and as a dashed line if it does not (greater than or less than).

Test Point Method

The test point method is a strategy used to determine which side of the boundary line should be shaded to represent the solution set of the inequality. By selecting an arbitrary point (often one that makes calculations simple) that is not on the boundary line and substituting its coordinates into the inequality, one can check if the inequality holds. If the test point satisfies the inequality, then the region containing that point is part of the solution set; otherwise, the opposite region should be shaded.

Shading Regions

Shading regions on the graph of a linear inequality is the final step in visually representing all the solutions to the inequality. Once the direction of the inequality is determined using methods such as the test point method, the corresponding half-plane is shaded. This shaded area indicates all the points at (x, y) that meet the conditions of the inequality, making it easy to visualize the solution set.

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