/*! 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 52 Graph equation in a rectangular ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 52

Graph equation in a rectangular coordinate system. $$x=5$$

Short Answer

Expert verified
The graph of the equation \(x=5\) is a vertical line passing through points where the x-coordinate is 5.

Step by step solution

01

Identify the type of line

Since the equation is \(x=5\) where there is no \(y\) variable present, this is a vertical line.
02

Plotting the line

In a rectangular coordinate system, plot a vertical line at x=5. This means the line passes through values where x is 5 on the x-axis. It will extend infinitely in both positive and negative y directions.
03

Mark the points

You can mark some points on the line to make it clear that all the points on this line have x-coordinate as 5. For instance, points could be (5,0), (5, 2), (5,-2), (5,4) etc. All these points will lie on the line \(x=5\).

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.

Rectangular Coordinate System
The rectangular coordinate system, also known as the Cartesian coordinate system, is a foundation for graphing. This system uses two perpendicular lines, usually denoted as the x-axis (horizontal) and the y-axis (vertical), to divide the plane into four regions called quadrants. Each point in this system can be described by an ordered pair, \((x, y)\). Here,
  • x represents the horizontal position.
  • y represents the vertical position.
When graphing, the intersection of these axes is called the origin and is designated by \((0, 0)\). The x-axis is aligned to increase from left to right, while the y-axis extends upwards and downwards. Being familiar with this setup is crucial for effectively locating and plotting points in graphing activities.
Vertical Line
A vertical line in a graph's rectangular coordinate system represents a constant x-value for all points on this line. In the equation \(x = 5\), the line is vertical because the value of x does not change regardless of the y-value. This contrasts with horizontal lines, which keep y constant while x can vary.Vertical lines have some unique characteristics:
  • They are parallel to the y-axis.
  • They do not have a slope, as their slope is considered undefined.
  • All points have the same x-coordinate.
Such lines extend infinitely upwards and downwards, going through points like \((5, 1)\), \((5, -2)\), and any other pair where the x-coordinate is 5. Understanding how to graph vertical lines helps interpret equations without a y-term.
Plotting Points
Plotting points effectively on the rectangular coordinate system is crucial for drawing precise graphs. To plot a point, you need an ordered pair \((x, y)\). This pair tells you exactly where to place a point on the graph.Here's how you plot points:
  • Start at the origin \((0, 0)\).
  • Move x units along the x-axis. If x is positive, move right; if negative, move left.
  • From that position, move y units parallel to the y-axis. Move up for positive y, down for negative y.
As an example, plotting the line \(x = 5\) involves just fixing your x-move to 5 and varying y to any value. Select some helpful points like \((5, 0)\), \((5, 3)\), and \((5, -4)\). All these points reinforce the concept of a vertical line at x = 5. Once plotted, these points illustrate the line visually, helping reinforce understanding the graphing process.

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

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+12 x-6 y-4=0$$

In your own words, describe how to find the midpoint of a line segment if its endpoints are known.

What does it mean if a function \(f\) is increasing on an interval?

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{3}-6 x^{2}+9 x+1$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. To avoid sign errors when finding \(h\) and \(k,\) I place parentheses around the numbers that follow the subtraction signs in a circle's equation.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

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.