/*! 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 34 For each equation, find the slop... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 34

For each equation, find the slope. If the slope is undefined, state this. $$ g(x)=-3 $$

Short Answer

Expert verified
The slope is 0.

Step by step solution

01

Identify the Equation Type

The given equation is a linear equation of the form \(g(x) = -3\). This represents a horizontal line.
02

Understand the Slope of a Horizontal Line

For any horizontal line which has the form \(y = c\), where \(c\) is a constant, the slope is always zero because there is no change in the \(y\)-value as the \(x\)-value changes.
03

Determine the Slope

Since \(g(x) = -3\) is a horizontal line, the slope of the line is \(0\).

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.

Linear Equations
In mathematics, a linear equation is any equation that can be written in the form: \[ y = mx + b \] Here, \( m \) represents the slope of the line and \( b \) represents the y-intercept. Linear equations are called 'linear' because when graphed, they produce a straight line. They are fundamental in algebra and appear in various real-world applications.
  • The slope \( m \) indicates how steep the line is.
  • The y-intercept \( b \) shows where the line crosses the y-axis.
Learning to identify and work with linear equations helps in fields ranging from basic algebra to advanced calculus. When the line is horizontal or vertical, this basic form can slightly change, which leads us to our next core concept.
Horizontal Line
Horizontal lines are special kinds of lines in the coordinate plane. They run parallel to the x-axis and can be represented by an equation of the form: \[ y = c \] Here, \( c \) is a constant. The key feature of a horizontal line is that it has a constant y-value and the slope of a horizontal line is always zero. This is because:
  • The y-value does not change no matter what the x-value is.
  • Since the slope \( m \) is calculated by the change in y divided by the change in x (\( \frac{\text{螖}y}{\text{螖}x} \)), if \( \text{螖}y = 0 \), then the slope is zero.
Identifying horizontal lines and understanding their properties is a crucial part of solving and graphing linear equations.
Constant Function
A constant function is one of the simplest types of functions in mathematics. It can be written as: \[ f(x) = c \] Here, \( c \) is a constant. This means that the output value of the function is the same regardless of the input value. Constant functions graph as horizontal lines in the coordinate plane. For example, in the equation \( g(x) = -3 \), \( -3 \) is the constant output for any input \( x \). This kind of function is important because:
  • It represents situations where a quantity does not change.
  • It helps in understanding more complex functions later on.
Knowing how to recognize and interpret constant functions lays the groundwork for more advanced topics in mathematics.

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

Assume that \(r, p,\) and \(s\) are nonzero constants and that \(x\) and \(y\) are variables. Determine whether each equation is linear. $$ r^{2} x=p y+5 $$

Find \(k\) such that the line containing \((-3, k)\) and (4,8) is parallel to the line containing (5,3) and (1,-6)

Graph equation after plotting at least 10 points. \(y=\sqrt{x}+1 ;\) use \(x\) -values from 0 to 10

Write an equation, in standard form, for the line whose \(x\) -intercept is 5 and whose \(y\) -intercept is \(-4\)

Solve. If appropriate, classify the equation as either \(a\) contradiction or an identity. $$ 9-6(x-7)=12 $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

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.