/*! 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 21 Use the given conditions to writ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 21

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(=\frac{1}{2},\) passing through the origin

Short Answer

Expert verified
The point-slope form and slope-intercept form of the given line is \(y = \frac{1}{2}x\).

Step by step solution

01

Write the Point-Slope Form of a Line

The point-slope form of a line is given as \(y - y_1= m(x-x_1)\). In this scenario, the slope (\(m\)) is \(\frac{1}{2}\) , and the point through which the line passes (\(x_1, y_1\)) is (0,0), so the equation becomes \(y - 0 = \frac{1}{2}(x - 0)\). Simplifying this equation, we get \(y = \frac{1}{2}x\).
02

Write the Slope-Intercept Form of a Line

The slope-intercept form of a line is usually represented as \(y = mx + b\), where \(m\) is the slope, and \(b\) is the y-intercept. Given the slope (\(m = \frac{1}{2}\)), and knowing that our line passes through the origin, we know that \(b = 0\). Thus, replacing \(m\) and \(b\) in the equation, we get \(y = \frac{1}{2}x + 0\). This simplifies to the same equation: \(y = \frac{1}{2}x\).

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!

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

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. $$ f(x)=x^{3}-6 x^{2}+9 x+1 $$

In Exercises \(105-108,\) you will be developing functions that model given conditions. A chemist working on a flu vaccine needs to mix a \(10 \%\) sodium-iodine solution with a \(60 \%\) sodium-iodine solution to obtain a 50 -milliliter mixture. Write the amount of sodium iodine in the mixture, \(S,\) in milliliters, as a function of the number of milliliters of the \(10 \%\) solution used, \(x .\) Then find and interpret \(S(30)\)

determine whether each statement makes sense or does not make sense, and explain your reasoning. The equation of the circle whose center is at the origin with radius 16 is \(x^{2}+y^{2}=16\)

Suppose that a function \(f\) whose graph contains no breaks or gaps on \((a, c)\) is increasing on \((a, b),\) decreasing on \((b, c)\) and defined at \(b\). Describe what occurs at \(x=b\). What does the function value \(f(b)\) represent?

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ (x+1)^{2}+y^{2}=25 $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Applied 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.