Chapter 4: Q. 702 (page 576)

Write the inequality shown by the graph with the boundary line $y = - x - 3$

Short Answer

Expert verified

The inequality is $y \geq - x - 3$ .

Step by step solution

Step 1. Given information

Given equation $y = - x - 3$ .

Given graph

Step 2. Find the inequality representing the shaded region

The line $y = - x - 3$ is the boundary line.

On one side of the line are the points with $y > - x - 3$ and on the other side of the line are the points with $y < - x - 3$ .

Let’s test the point $(0, 0)$ and see which inequality describes its side of the boundary line.

At $(0, 0)$ , which inequality is true:

$y > - x - 3 0 > - 0 - 3 0 > - 3$ or $y < - x - 3 0 < - 0 - 3 0 < - 3$

So the side with $(0, 0)$ is the side where $y > - x - 3$ .

Step 3. Checking for (0,0)

We need to find the inequality for the region that does not contain $(0, 0)$ .

Since the boundary line is graphed as a solid line, the inequality will include an equal sign.

The graph shows the solution to the inequality $y \geq - x - 3$ .

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Write the inequality shown by the graph with the boundary line $y = - x - 3$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the inequality representing the shaded region

Step 3. Checking for (0,0)

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Write the inequality shown by the graph with the boundary liney=-x-3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the inequality representing the shaded region

Step 3. Checking for (0,0)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Logic and Functions

Calculus

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Write the inequality shown by the graph with the boundary line $y = - x - 3$