/*! 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 20 Find an equation of the given li... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 20

Find an equation of the given line. Horizontal through \((\sqrt{7}, 2)\)

Short Answer

Expert verified
The equation of the horizontal line through (\(\sqrt{7}\), 2) is \(y = 2\).

Step by step solution

01

Identify the Type of Line

A horizontal line has the same y-coordinate for all points on the line. Hence, for this problem, the y-coordinate will be constant.
02

Determine the Equation

Since the given point is \((\sqrt{7}, 2)\), the y-coordinate is 2. Thus, the equation of the line where y is always 2 is simply \ y = 2 \.

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.

Coordinates
Coordinates are fundamental in geometry and are used to locate points on a plane. A coordinate pair is written as \(x, y\) where \(x\) represents the position along the x-axis and \(y\) represents the position along the y-axis.
In our example, the given point is \(\textbackslash sqrt{7}, 2\). The first value \(\textbackslash sqrt{7}\) is the x-coordinate, indicating the position along the horizontal axis.
The second value, 2, is the y-coordinate and refers to the position along the vertical axis.
It is crucial to understand that the order in coordinates matters. \(x\) comes first, then \(y\). Misplacing these values can lead to errors in graphing and calculations.
Constant y-coordinate
A constant y-coordinate means that no matter what value the x-coordinate takes, the y-coordinate remains unchanged. This is the characteristic property of horizontal lines.
For the given point \( (\textbackslash sqrt{7}, 2) \), the y-coordinate is 2. This y-value remains 2 regardless of what the x-coordinate becomes. As such, all points on this horizontal line will have a y-coordinate of 2.
Understanding this property simplifies the process of identifying horizontal lines and determining their equations.
This fundamental concept makes it easy to form the line equation when you recognize a constant y-coordinate.
Line Equation
The equation of a horizontal line is straightforward as it represents a constant y-value for all x-coordinates. The general form for a horizontal line's equation is \y = c\, where \c\ is a constant y-value.
In our example, since the y-coordinate is always 2, the equation of the line is given by:
\[ y = 2 \]
This indicates that at any point along this line, the y-coordinate remains 2 while the x-coordinate can vary.
This simplicity in the equation of a horizontal line makes it one of the easiest to understand and plot.

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

An analysis of the daily output of a factory assembly line shows that about \(60 t+t^{2}-\frac{1}{12} t^{3}\) units are produced after \(t\) hours of work, \(0 \leq t \leq 8\). What is the rate of production (in units per hour) when \(t=2 ?\)

Use limits to compute the following derivatives. \(f^{\prime}(0)\), where \(f(x)=x^{3}+3 x+1\)

Compute the following limits. \(\lim _{x \rightarrow \infty} \frac{x^{2}+x}{x^{2}-1}\)

Rates of Change Suppose that \(f(x)=-6 / x .\) (a) What is the average rate of change of \(f(x)\) over each of the intervals 1 to 2,1 to \(1.5\), and 1 to \(1.2 ?\) (b) What is the (instantaneous) rate of change of \(f(x)\) when \(x=1 ?\)

The revenue from producing (and selling) \(x\) units of a product is given by \(R(x)=3 x-.01 x^{2}\) dollars. (a) Find the marginal revenue at a production level of 20 . (b) Find the production levels where the revenue is \(\$ 200\).
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.