/*! 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 72 Find the slope of each line, and... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 72

Find the slope of each line, and sketch its graph. $$ y=-4 $$

Short Answer

Expert verified
The slope is 0.

Step by step solution

01

- Identify the Equation

The given equation is in the form of y = k, where k is a constant. Here, the equation is y = -4.
02

- Understand Horizontal Line

For any equation of the form y = k, the graph is a horizontal line passing through the y-axis at k. In this case, the graph will be a horizontal line passing through y = -4.
03

- Determine the Slope

The slope of a horizontal line is always 0 since there is no vertical change as you move along the line (the rise is 0). Hence, the slope is 0.
04

- Sketch the Graph

To sketch the graph, draw a horizontal line that crosses the y-axis at the point (0, -4). This line extends infinitely in both the positive and negative directions along the x-axis.

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.

Horizontal Line
Understanding what a horizontal line is is fundamental. A horizontal line is a straight line parallel to the x-axis in a coordinate plane. For any equation given in the form of y = k, where k is a constant, the graph will always depict a horizontal line. For example, in the equation y = -4, the line is straight and passes through the point where y equals -4.
This line will not slant or tilt; it remains perfectly flat, stretching left and right infinitely. Here, the y-value remains constant at -4, regardless of any changes in the x-value.
Slope of a Line
The slope of a line measures its steepness. It's calculated as the change in the y-values divided by the change in the x-values (rise over run). In mathematical terms, slope m can be represented as:
\[ m = \frac{\text{change in } y}{\text{change in } x} \]
For horizontal lines, like our example y = -4, there is no vertical change as we move along the line. The rise is zero while the run changes, resulting in a slope (m) of:
\[ m = \frac{0}{\text{run}} = 0 \]
Hence, all horizontal lines, no matter where they are positioned on the graph, have a slope of 0. This means there is no incline and the line runs flat.
Graphing Equations
Graphing equations is a way to visually represent solutions to equations. Starting with simple equations such as y = -4 helps to understand the concept. Here's a step-by-step on how to graph it:
1. **Identify the equation**: Here, y = -4, meaning every point on this line has a y-coordinate of -4.
2. **Plot the y-intercept**: The line intersects the y-axis at (0, -4).
3. **Draw a horizontal line**: From the point (0, -4), draw a straight line extending infinitely to the left and right along the x-axis.
By following these steps, you ensure the line accurately represents the equation y = -4. Graphing equips you with a powerful visual tool to interpret linear equations.

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

Solve each system by the elimination method. Check each solution. $$ \begin{array}{l} 9 x+4 y=-3 \\ 6 x+6 y=-7 \end{array} $$

Braving blizzard conditions on the planet Hoth, Luke Skywalker sets out in his snow speeder for a rebel base \(4800 \mathrm{mi}\) away. He travels into a steady headwind and makes the trip in \(3 \mathrm{hr}\). Returning, he finds that the trip back, now with a tailwind, takes only \(2 \mathrm{hr}\). Find the rate of Luke's snow speeder and the wind speed.

How many pounds of candy that sells for \(\$ 2.50\) per \(1 \mathrm{~b}\) must be mixed with candy that sells for \(\$ 1.75\) per \(\mathrm{lb}\) to obtain \(6 \mathrm{lb}\) of a mixture that sells for \(\$ 2.10\) per lb?

During the \(2016-2017\) NHL regular season, the Anaheim Ducks played 82 games. Their wins and overtime losses resulted in a total of 105 points. They had 10 more losses in regulation play than overtimes losses. How many wins, losses, and overtime losses did they have that season?

Graph each line passing through the given point and having the given slope $$ (2,-5) ; m=0 $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

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.