/*! 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 19 Use the given conditions to writ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 19

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

Short Answer

Expert verified
The equation of the line in point-slope form is \(y + 2 = -x - 1/2\). In slope-intercept form, it is \(y = -x - 5/2\).

Step by step solution

01

Identify slope and given point

The slope of the line is given as -1 and the line passes through the point (-1/2, -2). These two pieces of information will allow us to write the equation in both forms.
02

Write the Point-Slope form

Using the point-slope form \(y-y_1=m(x-x_1)\), substitute \(m=-1, x_1= -1/2,\) and \(y_1=-2\). After substituting these values, the equation becomes \(y - (-2) = -1(x -(-1/2))\) which simplifies to \(y + 2 = -1(x +1/2)\). You can further simplify this to get \(y + 2 = -x - 1/2\). This is the point-slope form of the line.
03

Write the Slope-Intercept form

For the slope-intercept form, solve the equation from Step 2 for \(y\). This will give \(y = -x - 1/2 - 2\) which simplifies to \(y = -x - 5/2\). This is the slope-intercept form of the line.

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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. My body temperature is a function of the time of day.

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. $$ f(x)=x^{\frac{1}{3}}(x-4) $$

write the standard form of the equation of the circle with the given center and radius. $$ \text { Center }(-1,4), r=2 $$

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. $$ g(x)=x^{\frac{2}{3}} $$

complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}-2 x+y^{2}-15=0 $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.