/*! 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 91 What does a dashed line mean in ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 91

What does a dashed line mean in the graph of an inequality?

Short Answer

Expert verified
A dashed line in a graph of an inequality signifies that the points on the line itself are not included in the solution set of the inequality. It is used for 'less than' or 'greater than' relations.

Step by step solution

01

Understanding Graphs for Inequalities

When graphing inequalities, a line is used to visually distinguish two sections of a graph. These sections would be the set of points that satisfy the inequality, versus the set that does not. A dashed or a solid line is drawn based on whether or not the points on that line meet the inequality's conditions. The graph will include a shaded region, which represents all the solutions to an inequality.
02

Understanding Dashed Lines

A dashed line in the graph of an inequality means the points lying on the line itself are not included in the solution of the inequality. It is used when the inequality is 'less than' or 'more than', but not 'more than or equal to' or 'less than or equal to'. The dashed line just represents the boundary between the solutions and non-solutions, but doesn't include any solutions itself.
03

Application

For instance, when graphing the inequality \(y > 2x + 1\), it would be represented by a dashed line because points on the line \(y = 2x + 1\) don't satisfy the inequality. The shaded region (representing the solution) would be the part of the graph above this boundary line.

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!

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

This will help you prepare for the material covered in the next section. In each exercise, graph the linear function. $$f(x)=-\frac{2}{3} x$$

What is a solution of a system of linear inequalities?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Without using any algebra, it's obvious that the nonlinear system consisting of \(x^{2}+y^{2}-4\) and \(x^{2}+y^{2}-25\) does not have real-number solutions.

What is an objective function in a linear programming problem?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I graphed a nonlinear system that modeled the orbits of Earth and Mars, and the graphs indicated the system had a solution with a real ordered pair.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure 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.