/*! 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 38 Decide whether the line is horiz... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 38

Decide whether the line is horizontal or vertical. Then graph the line. \(x=-5\)

Short Answer

Expert verified
The given line is a vertical line. To graph it, a straight line should be drawn at \(x = -5\).

Step by step solution

01

Identify the Type of Line

The equation given is \(x = -5\), which is of the form \(x = c\). This means that we're dealing with a vertical line, where every point on this line has an x-coordinate of -5.
02

Graph the Line

To graph this line, a straight vertical line needs to be drawn at \(x = -5\) on a coordinate plane. It doesn't matter what the y-coordinates are because they can take any value; the x-coordinate will always be -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.

Understanding Vertical Lines
Vertical lines are a fundamental concept in graphing. They have an equation of the form \(x = c\), where \(c\) is a constant. This means that:
  • Every point on the line has the same x-value, \(c\).
  • The y-values can be anything鈥攖hey are unrestricted.
Think of vertical lines as boundaries on the coordinate plane. Imagine a line drawn straight up and down at a particular x-coordinate. For example, if the line is \(x = -5\), every point along this line has an x-coordinate of -5. It's like an invisible barrier that runs parallel to the y-axis. When you see the equation \(x = -5\), you can be sure it represents a vertical line.
Exploring the Coordinate Plane
The coordinate plane is a two-dimensional surface on which we can graph points, lines, and curves. It is divided into four quadrants by the x-axis (horizontal) and y-axis (vertical). Here's what you need to know:
  • X-Axis: Divides the plane into top and bottom halves.
  • Y-Axis: Divides the plane into left and right halves.
  • Quadrants: Numbered counter-clockwise starting from the upper right quadrant.
Each point on the coordinate plane is identified by a pair of numbers, \((x, y)\), where \(x\) is the horizontal position and \(y\) is the vertical position. When graphing a line like \(x = -5\), you locate -5 on the x-axis and draw a straight line parallel to the y-axis. It's essential to grasp the layout of the coordinate plane to effectively graph and interpret lines.
Introduction to Equations of Lines
Equations of lines are mathematical representations of straight lines on the coordinate plane. They provide a way to describe the characteristics of a line:
  • The general form for a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
  • However, vertical lines deviate from this form. They use the equation \(x = c\), representing a vertical line at the position \(c\) on the x-axis.
This distinction is crucial as vertical lines do not have a slope as defined in the usual sense of rise over run. Their slope is considered undefined because a vertical change without horizontal movement results in division by zero. Recognizing the type of line based on its equation allows you to accurately graph and understand its behavior in the coordinate system.

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

Write an equation in standard form of the line that passes through the two points. $$(0,0),(2,0)$$

Write an equation of the line that passes through the points. (-2,-3),(0,4)

Without calculating, state whether the slope of the line through the points is positive, negative, zero, or undefined. (2,5),(4,1)

Write an equation of the line that passes through the points. (5,2),(4,3)

Write an equation in standard form of the line that passes through the two points. $$(1,4),(5,7)$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.