/*! 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 43 Find an equation of the vertical... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 43

Find an equation of the vertical line with \(x\) -intercept at \(3 .\)

Short Answer

Expert verified
The equation of the vertical line with \(x\)-intercept at 3 is \(x = 3\).

Step by step solution

01

Understanding the problem

The question asks for the equation of a vertical line. This shows that the \(x\) value is constant. The \(x\)-intercept is 3 which means that the \(x\) value of the line is 3 at all points.
02

Formulating the equation

Knowing that the \(x\) value for the line is constant and equal to the \(x\)-intercept point, an equation can be written as \(x = 3\).

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 the x-intercept
The x-intercept is a fundamental concept in algebra and refers to the point where a line crosses the x-axis. At the x-intercept, the y-value is always zero. This is because the line is crossing the axis where x is a specific value and y is 0.

In our exercise, the x-intercept is given as 3. This means our vertical line crosses the x-axis exactly at the point where x equals 3. For vertical lines, the x-intercept uniquely defines the position of the line on a graph since it does not have a slope or y-intercept like non-vertical lines do.
The constant x-value in a vertical line
In the context of vertical lines, the x-value remains constant. This means that no matter where you are on the line, the x-coordinate will always be the same.

For the vertical line with an x-intercept at 3, the x-coordinate is constantly 3 for any point on that line. This property makes vertical lines unique compared to other types of lines.
  • They do not tilt or slope.
  • Their y-values can vary, but x remains unchanged.
Understanding the constant x-value helps in formulating the correct equation for the line.
Formulating the line equation
The line equation for vertical lines is straightforward due to the constant x-value. Since the x-coordinate doesn't change along a vertical line, the equation is simple.

For our line with an x-intercept of 3, we can write the equation as:\[x = 3\]This equation directly indicates that no matter where you look along the line, x will always be 3. This differs from horizontal lines where the equation might look like \(y = c\) with a constant y-value. Vertical line equations are a great example of direct and simple expressions in mathematics, where the x-value is concise and clear.

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

Prove that the figure formed by connecting consecutive midpoints of the sides of any quadrilateral is a parallelogram.

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \(f(x)=f(-x)\) for all \(x\) in the domain of \(f\), then the graph of \(f\) is symmetric with respect to the \(y\) -axis.

Use the Vertical Line Test to determine whether \(y\) is a function of \(x\). To print an enlarged copy of the graph, select the MathGraph button. $$y=\left\\{\begin{aligned} x+1, & x \leq 0 \\\\-x+2, & x>0 \end{aligned}\right.$$

Find the distance between the point and line, or between the lines, using the formula for the distance between the point \(\left(x_{1}, y_{1}\right)\) and the line \(A x+B y+\) \(C=0 .\) Point: \((-2,1)\) Line: \(x-y-2=0\)

Find the domain of the function. $$f(x)=\frac{1}{|x+3|}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Pure 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.