/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 264 Graph the linear inequality: \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 264

Graph the linear inequality: \(y \geq 2\)

Short Answer

Expert verified
The graph is a solid horizontal line at \(y = 2\) with the region above the line shaded.

Step by step solution

01

Understand the inequality

The given inequality is in the form of a linear inequality where the boundary line is given by the equation: \(y = 2\). The inequality \(y \geq 2\) means that we are looking for all values of \(y\) that are greater than or equal to 2.
02

Draw the boundary line

Graph the boundary line \(y = 2\). This line is horizontal and passes through all points where the \(y\)-coordinate is 2. Because the inequality symbol is \(\geq\), draw a solid line to show that points on the line are included in the solution.
03

Shade the solution region

Since the inequality is \(y \geq 2\), shade the region above the line \(y = 2\). This represents all the points where \(y\) is greater than or equal to 2.
04

Verify solution region

Pick a test point that is not on the boundary line to verify if it satisfies the inequality. For example, use the point \((0, 3)\). Since \(3 \geq 2\) is true, the region above the line is correct.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

linear inequalities
Linear inequalities are similar to linear equations but instead of an

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Harrison works two part time jobs. One at a gas station that pays \(\$ 11\) an hour and the other is IT troubleshooting for \(\$ 16.50\) an hour. Between the two jobs, Harrison wants to earn at least \(\$ 330\) a week. How many hours does Harrison need to work at each job to earn at least \(\$ 330 ?\) (a) Let \(x\) be the number of hours he works at the gas station and let \(y\) be the number of (hours he works troubleshooting. Write an inequality that would model this situation. (b) Graph the inequality. (c) Find three ordered pairs \((x, y)\) that would be solutions to the inequality. Then, explain what that means for Harrison.

In the following exercises, evaluate the function: (@) \(g\left(h^{2}\right)\) (b) \(g(x+2) @ g(x)+g(2) .\) $$ g(x)=7-5 x $$

In the following exercises, evaluate the function: (@) \(f(2)\) (b) \(f(-1)\) (c) \(f(a) .\) $$ f(x)=-6 x-3 $$

In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation.] $$ f(x)=x^{2}+1 $$

In the following exercises, evaluate the function: (@) \(f(2)\) (b) \(f(-1)\) (c) \(f(a) .\) $$ f(x)=3 x^{2}+x-2 $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.