/*! 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 68 Graph each equation. \(y=-5\) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 68

Graph each equation. \(y=-5\) (Section 3.2, Example 7)

Short Answer

Expert verified
The graph of the equation \(y=-5\) is a straight line parallel to the x-axis passing through points where y-coordinate is -5.

Step by step solution

01

Understand the equation

The equation given here is \(y=-5\). This is a linear equation where y is a constant. This means for all values of x, y will always be -5.
02

Plotting points on the graph

Since the y-coordinate remains -5 for all x-coordinates, we can pick any values for x and the corresponding y will always be -5. Let's pick few points, say x= -2, 0, 2, their corresponding y-values will be -5.
03

Drawing the graph

Join the points plotted on the Cartesian plane. The line passing through these points represents the graph of the given equation \(y=-5\). This is a horizontal line parallel to x-axis at y=-5.

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 Equations
A linear equation is a mathematical expression that forms a straight line when graphed on a coordinate plane. These equations take the general form of \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-intercept.
In simpler terms, a linear equation involves variables where the highest power of the variable is one. This means the relationship between the variables shows as a line.
**Key points about linear equations:**
  • They can represent real-world relationships, like speed and time.
  • The slope \(m\) tells us the steepness and direction of the line.
  • The y-intercept \(b\) is where the line crosses the y-axis.
For our example, though, the equation \(y = -5\) doesn't show a slope part. It is essentially "flat" in terms of slope, which leads us to explore the next concept.
Cartesian Plane
The Cartesian plane is a two-dimensional grid where linear equations get visualized. It comprises two perpendicular axes: the horizontal x-axis and the vertical y-axis. These intersect at a point called the origin, labeled as (0, 0).
**Understanding the axes:**
  • The x-axis runs left to right. Typically, positive numbers are on the right, and negative numbers are on the left.
  • The y-axis runs up and down. Positive numbers are upwards, and negative numbers are downwards.
When plotting linear equations like \(y = -5\), we mark points on this grid. Each point corresponds to a pair of values \((x, y)\). Since the equation states \(y = -5\) for any \(x\), the points would spread along a horizontal line. Understanding how these axes work helps us graph the equation efficiently.
Horizontal Lines
Horizontal lines on a graph are unique and straightforward. They occur when the y-value remains constant, regardless of the x-value. Our example, \(y = -5\), forms such a line.
**Characteristics of horizontal lines:**
  • The line's slope is zero, meaning it's completely flat.
  • These lines run parallel to the x-axis.
  • They intersect the y-axis at the point where the y-value is constant, here at \(y = -5\).
To graph a horizontal line, once you know the constant y-value, use any x-values. Plot the respective points, and they should align horizontally across the plane. Understanding horizontal lines simplify tasks like predicting the behavior of such equations and identifying them quickly on a 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

When using the addition method, how can you tell if a system of linear equations has no solution?

When using the substitution method, how can you tell if a system of linear equations has infinitely many solutions?

Solve each system by the method of your choice. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. Explain why you selected one method over the other two. $$\left\\{\begin{array}{l}y=2 x+4 \\ y=2 x-1\end{array}\right.$$

Tourist: "How many birds and lions do you have in your zoo? Zookeeper: "There are 30 heads and 100 feet." Tourist: "I can't tell from that." Zookeeper: "Oh, yes, you can!" Can you? Find the number of each.

You are choosing between two telephone plans. Plan A has a monthly fee of \(\$ 20\) with a charge of \(\$ 0.05\) per minute for all calls. Plan B has a monthly fee of \(\$ 5\) with a charge of \(\$ 0.10\) per minute for all calls. a. For how many minutes of calls will the costs for the two plans be the same? What will be the cost for each plan? b. If you make approximately 10 calls per month, each averaging 20 minutes, which plan should you select? Explain your answer.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.