Chapter 4: Q. 672 (page 573)

In the following exercises, write the inequality shown by the shaded region.
Write the inequality shown by the graph with the boundary line
$y = - x + 2$ .

Short Answer

Expert verified

The inequality shown by the graph is $y ⩽ - x + 2$ .

Step by step solution

Step 1. Given Information

A graph with boundary line $y = - x + 2$ is given.

We have to find the inequality the graph represents.

Step 2. Definition of a solution

An ordered pair $(x, y)$ is a solution of the linear inequality if the pair of values satisfy the inequality when substituted.

Step 3. Determining the inequality

The boundary line $y = - x + 2$ has one side of the points satisfying $y > - x + 2$ and other side satisfying $y < - x + 2$ .

Consider a point in the shaded area in the given graph.

Let us consider $(0, 0)$ .

Check which inequality the point $(0, 0)$ satisfies.

$y > - x + 2 \Rightarrow 0 > - 0 + 2 \Rightarrow 0 > 2$ False.

$y < - x + 2 \Rightarrow 0 < - 0 + 2 \Rightarrow 0 < 2$ True.

Since the boundary line is marked with a solid line, equal to sign is also included.

Therefore the inequality graph represents is $y ⩽ - x + 2$ .

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In the following exercises, write the inequality shown by the shaded region.
Write the inequality shown by the graph with the boundary line
$y = - x + 2$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Definition of a solution

Step 3. Determining the inequality

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In the following exercises, write the inequality shown by the shaded region.Write the inequality shown by the graph with the boundary liney=-x+2.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Definition of a solution

Step 3. Determining the inequality

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Statistics

Discrete Mathematics

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, write the inequality shown by the shaded region.
Write the inequality shown by the graph with the boundary line
$y = - x + 2$ .