/*! 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 11 Graph each linear inequality. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 11

Graph each linear inequality. \(y>\frac{1}{3} x\)

Short Answer

Expert verified
The graph of the inequality \(y > \frac{1}{3} x\) is a dashed line, representing \(y=\frac{1}{3}x\), with the area above this line shaded, indicating all the points that satisfy the given inequality.

Step by step solution

01

Identify the inequality

The given inequality is \(y > \frac{1}{3} x\). This inequality can be graphed on a coordinate plane.
02

Understand the inequality

Since the inequality is \(y>\frac{1}{3}x\), this means that we are looking for all the points (x, y) for which y is greater than \(\frac{1}{3}x\). In other words, we want all the points above the line \(y=\frac{1}{3}x\).
03

Graph the boundary line

First, graph the line \(y=\frac{1}{3}x\). This is a straight line with a slope of 1/3 and passing through the origin (0, 0). Because the inequality sign is strictly 'greater than' and not 'greater than or equal to', the line should be drawn as a dashed line. The dashed line signifies that points on the line are not included in the solution of the inequality.
04

Shading the solution region

Next, to denote the points for which y is greater than \(\frac{1}{3}x\), shade the region above the line. All the points in this shaded region are solutions to the inequality.

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

a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & -4 \\ \hline 1 & -1 \\ \hline 2 & 0 \\ \hline 3 & -1 \\ \hline 4 & -4 \\ \hline \end{array} $$

In Exercises 65-66, let \(f\) and \(g\) be defined by the following table: $$ \begin{array}{|c|c|c|} \hline \boldsymbol{x} & \boldsymbol{f}(\boldsymbol{x}) & \boldsymbol{g}(\boldsymbol{x}) \\ \hline-2 & 6 & 0 \\ \hline-1 & 3 & 4 \\ \hline 0 & -1 & 1 \\ \hline 1 & -4 & -3 \\ \hline 2 & 0 & -6 \\ \hline \end{array} $$ Find \(|f(1)-f(0)|-[g(1)]^{2}+g(1) \div f(-1) \cdot g(2)\)

Graph each linear inequality. \(y>-2\)

An important application of systems of equations arises in connection with supply and demand. As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The price at which supply and demand are equal is called the equilibrium price. The quantity supplied and demanded at that price is called the equilibrium quantity. Exercises 61-62 involve supply and demand. The following models describe demand and supply for threebedroom rental apartments. Demand Model Supply Model \(p=-50 x+2000\) \(p=50 x\) a. Solve the system and find the equilibrium quantity and the equilibrium price. b. Use your answer from part (a) to complete this statement: When rents are ____ per month, consumers will demand apartments and suppliers will offer _____ apartments for rent.

What is a constraint in a linear programming problem? How is a constraint represented?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

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.