/*! 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 211 In the following exercises, find... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 211

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope-intercept form. line \(x=3\), point (3,4)

Short Answer

Expert verified
y = 4

Step by step solution

01

- Identify the given line form

The given line equation is in the form of a vertical line: \(x = 3\). Vertical lines have an undefined slope.
02

- Understand the perpendicular line

A line perpendicular to a vertical line is a horizontal line. Horizontal lines have a slope of 0.
03

- Determine the equation using the given point

The given point is (3, 4). A horizontal line passing through this point will have the equation: \(y = 4\).
04

- Write the equation in slope-intercept form

For horizontal lines, the equation is already in slope-intercept form: \(y = mx + b\) where \(m = 0\) and \(b = 4\).Thus, the equation is \(y = 4\).

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.

Equation of a Line
Lines in mathematics are typically expressed using an equation.
This equation represents all the points that lie on the line.
One common form is the slope-intercept form, but there are others.
Here are a few key points to keep in mind:
  • An equation of a line shows the relationship between the x and y coordinates of points on the line.
  • This can be written in different ways, such as slope-intercept form or standard form.
  • Understanding these forms helps you identify and work with the line鈥檚 properties.
Slope-Intercept Form
The slope-intercept form is a common way to express the equation of a line.
It is written as: \(y = mx + b\)
Here, \(m\) represents the slope, and \(b\) represents the y-intercept of the line.
Let's delve into these components:
  • Slope (m): This indicates how steep the line is. A higher value means a steeper line. It can be positive, negative, zero, or even undefined in some cases.
  • Y-Intercept (b): This is the point where the line crosses the y-axis. When x=0, y equals b.

Using slope-intercept form makes it easy to quickly understand and graph a line.
Undefined Slope
Some lines have an undefined slope, which is an important concept to grasp.
Lines with undefined slopes are vertical lines.
Here are key points to remember:
  • A vertical line has the same x-coordinate for all its points.
  • The equation of a vertical line is in the form: \(x = c\) where 'c' is a constant.
  • These lines do not cross the y-axis and their slope is considered undefined.

For example, the line \(x = 3\) has an undefined slope because it runs parallel to the y-axis passing through all the points where x is 3.
Horizontal and Vertical Lines
Horizontal and vertical lines are unique types of lines.
They are straightforward to work with once you understand their properties:
  • Horizontal Lines: These lines have a slope of 0. They remain constant along the y-axis as they extend left and right. The equation form is \(y = c\) where 'c' is a constant.

  • Vertical Lines: As mentioned, these have an undefined slope. They extend up and down, maintaining a constant x-coordinate. Their equation is \(x = c\)

It's crucial to recognize these lines since they behave differently from lines with non-zero slopes.

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?

. Graph the linear inequality: \(y \leq \frac{5}{4} x\)

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

In the following exercises, evaluate the function. $$ h(t)=2|t-5|+4 ; h(-4) $$

Armando's workouts consist of kickboxing and swimming. While kickboxing, he burns 10 calories per minute and he burns 7 calories a minute while swimming. He wants to burn 600 calories each day. (a) If \(x\) is the number of minutes that Armando will kickbox and \(y\) is the number minutes he will swim, find the inequality that will help Armando create a workout for today. (b) Graph the inequality. (c) List three solutions to the inequality. What options do the solutions provide Armando?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Statistics

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.