/*! 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 49 Graph equation in a rectangular ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 49

Graph equation in a rectangular coordinate system. $$y=-2$$

Short Answer

Expert verified
The graph of the equation 'y=-2' is a horizontal line parallel to the x-axis, crossing the y-axis at -2.

Step by step solution

01

Set Up the Coordinate System

Draw a rectangular or Cartesian coordinate system. The x-axis (horizontal) and y-axis (vertical) intersect at a point called the origin. The positive direction for x is to the right and for y is upwards.
02

Identify the Line Equation

The given equation is y = -2. This is a horizontal line, parallel to x-axis, crossing the y-axis at -2.
03

Plot the Line

Using a ruler, draw a horizontal line across the graph that intersects the y-axis at -2. All the points along this line have y-coordinate equal to -2. This line represents the graph of the equation.

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.

Coordinate System
A coordinate system is a grid that helps us locate points on a plane. In a 2D space, the most commonly used coordinate system is the Cartesian plane, which consists of two main components:
  • The x-axis, which is a horizontal line.
  • The y-axis, which is a vertical line.
These two lines intersect at a point called the origin, noted as (0, 0). The plane is divided into four quadrants by these axes. Each point in this system is defined by a pair of numbers, \(x, y\), called coordinates. The x value shows the point's distance from the y-axis, while the y value shows its distance from the x-axis. Together, they allow us to pinpoint exact locations on the graph. Understanding the coordinate system is crucial for plotting and graphing equations effectively.
Horizontal Line
A horizontal line on a graph runs left to right, parallel to the x-axis. In the equation form, a horizontal line can be represented as \(y = c\), where \(c\) is a constant. This equation means that no matter what value x takes, y remains the same.
For instance, in the equation \(y = -2\), every point on this line has a y-coordinate of -2.
  • The line cuts across the graph, intersecting the y-axis at -2.
  • It does not intersect the x-axis because its y-value does not change with x.
Horizontal lines are unique in that their slope is zero, indicating that there is no vertical change when moving along the line. This is important to know when dealing with linear equations and graph interpretations.
Plotting Points
Plotting points on a graph involves locating each point on the coordinate plane using their respective coordinates \(x, y\). Here鈥檚 how you can plot points effectively:
  • Start at the origin (0,0).
  • Move horizontally to the x-coordinate value.
  • Then, move vertically to reach the y-coordinate value.
Once you reach the exact spot, you mark it with a dot. To graph a line like \(y = -2\), you need several points that satisfy the equation. However, since \(y = -2\) is a horizontal line, any points have the same y-coordinate value (-2).
For example, some points \( (1, -2), (0, -2), (-1, -2) \) can be plotted anywhere along this line. Thus, once a few of these points are plotted, they can be connected to show the full extent of the line across the graph.

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

If you are given a function's equation, how do you determine if the function is even, odd, or neither?

Determine whether each statement makes sense or does not make sense, and explain your reasoning.I used a function to model data from 1990 through 2015 .I have two functions. Function \(f\) models total world population \(x\) years after 2000 and function \(g\) models population of the world's more-developed regions \(x\) years after 2000.1 can use \(f-g\) to determine the population of the world's less-developed regions for the years in both function's domains.

Will help you prepare for the material covered in the next section. $$\text { If }\left(x_{1}, y_{1}\right)=(-3,1) \text { and }\left(x_{2}, y_{2}\right)=(-2,4), \text { find } \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$

A department store has two locations in a city. From 2012 through \(2016,\) the profits for each of the store's two branches are modeled by the functions \(f(x)=-0.44 x+13.62\) and \(g(x)=0.51 x+11.14 .\) In each model, \(x\) represents the number of years after \(2012,\) and \(f\) and \(g\) represent the profit, in millions of dollars. a. What is the slope of \(f ?\) Describe what this means. b. What is the slope of \(g\) ? Describe what this means. c. Find \(f+g .\) What is the slope of this function? What does this mean?

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-10 x-6 y-30=0$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.