Chapter 4: Q. 4.141 (page 550)

Write the inequality shown by the shaded region in the graph with the boundary line $x - 4 y = 8$

Short Answer

Expert verified

The inequality shown by the graph is $x - 4 y \leq 8$ .

Step by step solution

Step 1. Given Information

We are given an equation $x - 4 y = 8$ and a graph,

Step 2. Finding the inequality

The line $x - 4 y = 8$ is the boundary line. On one side of the line are the points with $x - 4 y > 8$ and on the other side of the line are the points with $x - 4 y < 8$ .

Checking the inequality with point $(0, 0)$ ,

$x - 4 y > 8 0 - 4 (0) > 8 0 > 8$

False.

Step 3. Finding the inequality

Checking the inequality with point $(0, 0)$ ,

localid="1647587517869" $x - 4 y < 8 0 - 4 (0) < 8 0 < 8$

True.

Since $x - 4 y < 8$ is true for the point $(0, 0)$ which is the part of shaded region, hence shaded region is the solution for the inequality $x - 4 y < 8$

Also, the boundary line is graphed with a solid line, the inequality includes the equal sign.

$x - 4 y \leq 8$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write the inequality shown by the shaded region in the graph with the boundary line $x - 4 y = 8$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the inequality

Step 3. Finding the inequality

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Write the inequality shown by the shaded region in the graph with the boundary line x−4y=8

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the inequality

Step 3. Finding the inequality

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Write the inequality shown by the shaded region in the graph with the boundary line $x - 4 y = 8$