Chapter 3: Q272. (page 312)

Graph the linear inequality:
$y < - 3 x - 4$

Short Answer

Expert verified

The solution is

Step by step solution

Given data

The inequality is

$y < - 3 x - 4$

Concept used

First, we draw the boundary line $y = - 3 x - 4$ .

It is in slope-intercept form with $m = - 3$ and $b = - 1$ .

Here the inequality is $<$ .

So, we draw a dashed line as bellow,

Point test

We can see that the point $(0, 0)$ is not on boundary line.

To check $(0, 0)$ is a solution of the inequality or not:

$y < - 3 x - 4$

$0 < - 3 \cdot 0 - 4$

$0 < 0 - 4$

$0 < - 4$

Which is not possible.

So, $(0, 0)$ is not a solution of the inequality $y < - 3 x - 4$ .

Conclusion

Thus, we shade in the side of the boundary line that does not include the point $(0, 0)$ .

The graph will be

All points in the shaded region, but not those on the boundary line, represent the solutions to $y < - 3 x - 4$ .

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.

Graph the linear inequality:
$y < - 3 x - 4$

Short Answer

Step by step solution

Given data

Concept used

Point test

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Decision Maths

Statistics

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

Graph the linear inequality: y<-3x-4

Short Answer

Step by step solution

Given data

Concept used

Point test

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Decision Maths

Statistics

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

Graph the linear inequality:
$y < - 3 x - 4$