/*! 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 84 In the following exercises, find... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 84

In the following exercises, find the slope of each line. $$ x=4 $$

Short Answer

Expert verified
The slope of a vertical line is undefined.

Step by step solution

01

Recognize the Type of Line

Identify the type of line given by the equation. The equation is of the form \(x = 4\), which represents a vertical line.
02

Recall the Slope of a Vertical Line

Recall that the slope of a vertical line is always undefined. This is because a vertical line does not change in the \(y\) direction no matter how much it changes in the \(x\) direction.

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.

Vertical Lines
Vertical lines are unique in the world of coordinate geometry. They are represented by equations like \( x = a \), where \( a \) is a constant. In these equations, \( x \) never changes no matter what the value of \( y \) is. For example, the equation \( x = 4 \) tells us that this line passes through every point that has an \( x \)-coordinate of 4. Here, the \( y \)-coordinate can be any value, but \( x \) remains constant at 4. This attribute of vertical lines makes them stand out and impacts their slope significantly.
Slope of a Line
The slope of a line is a measure of its steepness and direction. Mathematically, it is defined as the rise over the run. In other words, it is the change in the \( y \) direction divided by the change in the \( x \) direction, given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]. However, when dealing with vertical lines, the situation is different. Because the \( x \) value does not change, the denominator in the slope formula becomes zero. This leads us to a special case of slope. For most lines, the slope gives us valuable information about how the line angles.
Undefined Slope
The undefined slope occurs specifically in vertical lines. Because vertical lines do not spread horizontally (their \( x \) coordinates remain constant), the term \( x_2 - x_1 \) in the slope formula becomes zero. Division by zero is undefined in mathematics and it makes the slope of vertical lines undefined as well. This characteristic is a key feature of vertical lines and sets them apart from other lines which have defined slopes. Understanding why the slope is undefined helps in recognizing vertical lines and dealing with various geometrical problems that involve them.

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

Is every relation a function? Is every function a relation?

In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. $$ f(x)=\frac{1}{2} x^{2} $$

Graph the linear inequality: \(x-y<4\)

In the following exercises, evaluate the function. \(g(x)=\frac{x-2}{x+2} ; g(4)\)

In the following exercises, (a) graph each function (b) state its domain and range. Write the domain and range in interval notation. $$ f(x)=-2 x^{3} $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.