/*! 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 62 Find the slope of each line. See... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 62

Find the slope of each line. See Examples 4 and \(5 .\) $$y=-2$$

Short Answer

Expert verified
The slope of the line is 0.

Step by step solution

01

Identifying the Line Type

The given equation is \( y = -2 \). This equation represents a horizontal line, as it is in the form \( y = c \), where \( c \) is a constant.
02

Understanding the Slope of Horizontal Lines

By definition, the slope of a horizontal line is 0. This is because the line runs parallel to the x-axis and doesn't rise at all as it moves right.
03

Conclusion

The slope of the line represented by the equation \( y = -2 \) is 0, as horizontal lines always have a slope of 0.

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 Lines
When we talk about horizontal lines in the context of graphs and geometry, these are lines that run from left to right across the Cartesian plane. They are parallel to the x-axis and therefore have no vertical change as you move along the line.
A horizontal line can be recognized by its equation, which is always of the form \( y = c \), where \( c \) is a constant number. This tells you that no matter the value of \( x \), the value of \( y \) remains constant and equal to \( c \).
  • For example, the equation \( y = -2 \) is a horizontal line because it tells us that for any value of \( x \), \( y \) will always be -2.
Understanding horizontal lines helps in identifying their slope and writing linear equations related to them.
Linear Equations
A linear equation is an equation that can be graphically represented as a straight line. These equations typically look like \( y = mx + b \), where:
  • \( m \) is the slope of the line.
  • \( b \) is the y-intercept, or where the line crosses the y-axis.
However, linear equations can also take special forms. When you see an equation in the form \( y = c \), this suggests a horizontal line.
In such cases:
  • The slope \( m \) is 0 because there is no change in the \( y \)-value as \( x \) changes.
  • The y-intercept \( b \) is \( c \), because the line crosses the y-axis at this constant value.
Recognizing these forms helps in comprehending the behavior and geometry of lines in 2D space.
Slope Calculation
The slope of a line is a measure of its steepness and direction. It is calculated by the ratio of the vertical change (difference in \( y \)-values) to the horizontal change (difference in \( x \)-values) between two points on the line.
The formula for calculating the slope \( m \) is given by:
\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\]
However, for horizontal lines, like \( y = -2 \), the calculation simplifies significantly:
  • There is no change in the \( y \)-value regardless of how much the \( x \)-value changes, hence the vertical change \( (y_2 - y_1) \) is zero.
This means:
  • The slope of a horizontal line is \( m = 0 \), because dividing zero by any non-zero number gives a quotient of zero.
Understanding these characteristics helps you quickly determine the behavior of different types of lines and their corresponding slopes.

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

Graph the inequality: $$4 x-3(x+2 y-1) \geq-6\left(y-\frac{1}{2}\right)$$

If the graph of \(y=m x+b\) passes through quadrants I, II, and IV, what can be known about the constants \(m\) and \(b ?\)

Lightning. The function \(D(t)=\frac{t}{5}\) gives the approximate distance in miles that you are from a lightning strike, where \(t\) is the number of seconds between seeing the lightning and hearing the thunder. Find \(D(5)\) and explain what it means.

Find the slope of a line perpendicular to the line passing through the given two points. See Example \(9 .\) \((-1,2)\) and \((-3,6)\)

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. $$ 2 x+3 y=9 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Decision Maths

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.