/*! 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 575 Graph the equation \(\mathrm{xy}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 19: Problem 575

Graph the equation \(\mathrm{xy}=-4\).

Short Answer

Expert verified
To graph the equation \(xy =-4\), we first find ordered pairs (x, y) that satisfy the equation, such as (-1, 4), (-2, 2), (1, -4), and (2, -2). Plot these points on the Cartesian plane and connect them to sketch the hyperbola. The graph has two branches, one in the first and third quadrants and the other in the second and fourth quadrants, indicating that the product of x and y is negative.

Step by step solution

01

Select values for x and find corresponding y values

We will start by selecting a few values for x and finding the corresponding values for y that satisfy the equation \(xy = -4\). For example, let's select x=-1, x=-2, x=1, and x=2 as our x values. Using these x values, we can find the y values as follows: 1. When x=-1, y=(-1)*(-4)= 4 2. When x=-2, y=(-2)*(-2)= 2 3. When x=1, y=(1)*(-4)= -4 4. When x=2, y=(2)*(-2)= -2 So, we have the ordered pairs (-1,4), (-2,2), (1,-4), and (2,-2).
02

Plot the ordered pairs on the Cartesian plane

Now that we have a few ordered pairs, the next step is to plot them on the Cartesian plane. These points will help us sketch the graph of the equation. 1. Plot the point (-1, 4) 2. Plot the point (-2, 2) 3. Plot the point (1, -4) 4. Plot the point (2, -2)
03

Sketch the graph of the equation

As we connect the plotted points, we can observe that the graph of the equation \(xy=-4\) is a hyperbola with its center at the origin (0,0). The hyperbola has two branches, one in the first and third quadrants and the other in the second and fourth quadrants, indicating that the product of x and y is negative. To better visualize the graph, you can create more points by selecting different x values and finding the corresponding y values using the equation \(xy = -4\). The more points you plot, the more accurate your graph will be.

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

Discuss the graph of \(\mathrm{x}^{2} / 9-\mathrm{y}^{2} / 9=1\)

Find the equation for the circle whose center is at the origin and whose radius is 3 .

The surface \(\mathrm{S}\) of a cube is given by the formula \(\mathrm{S}=6 \mathrm{x}^{2}\) where \(\mathrm{x}\) represents the length of an edge. Graph \(\mathrm{S}\) as a function, of \(\mathrm{x}\).

Sketch the graph of the equation \(\mathrm{x}^{2}+\mathrm{y}^{2}=4\)

Construct a graphical representation of the inequality \(\mathrm{x}^{2}-2 \mathrm{x}-8 \leq 0\) and identify the solution set.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.