In Exercises 5-18, sketch the graph of the inequality. y<2-x...

Name: Problem 11, Chapter 7: Precalculus with Limits
Uploaded: 2021-05-21T19:51:56-08:00
Duration: 3 min 10 s
Channel: Alex Roush
Description: In Exercises 5-18, sketch the graph of the inequality. y<2-x

Key Concepts

Graphing Linear Inequalities

Graphing linear inequalities involves plotting a straight line corresponding to the equality part and then determining which side of the line satisfies the inequality. This process typically includes evaluating the inequality at a test point to decide the appropriate region to shade on the coordinate plane.

Boundary Lines

The boundary line is derived from the associated equation of the inequality. It acts as the edge of the region described by the inequality. In this context, the line separates the parts of the plane that satisfy the inequality from those that do not.

Open vs Closed Boundary

For inequalities, the type of boundary line used depends on whether the inequality is strict or non-strict. A strict inequality, like the one in this problem, requires a dashed boundary line, indicating that points on the line are not included in the solution set, while a non-strict inequality would use a solid line.

Shading Regions

Shading the region of a graph is used to visually represent the set of all points that satisfy the inequality. This involves choosing a test point from either side of the boundary line to determine which region should be shaded, ensuring that the graphical solution accurately reflects the inequality's condition.

Test Point Method

The test point method is a technique used to verify which half of the divided plane satisfies the inequality. By substituting the coordinates of a point (usually not on the boundary) into the inequality, one can confirm whether the point lies in the solution set, thereby identifying the correct region to shade.

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