/*! 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 45 Find an equation of the line tha... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 45

Find an equation of the line that passes through the point \((-2,2)\) and is parallel to the line \(2 x-4 y-8=0\).

Short Answer

Expert verified
The equation of the line that passes through the point \((-2, 2)\) and is parallel to the line \(2x - 4y - 8 = 0\) is \(\boxed{y = \frac{1}{2}x + 3}\).

Step by step solution

01

Determine the slope of the given line

To determine the slope of the line \(2x - 4y - 8 = 0\), let's first rewrite the equation in slope-intercept form. The slope-intercept form of a linear equation is \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-intercept. Starting with the equation \(2x - 4y - 8 = 0\), isolate y as follows: \(4y = 2x - 8\) \(y = \frac{1}{2}x - 2\) Now that the equation is in slope-intercept form, we can see that the slope of the line is \(m = \frac{1}{2}\).
02

Use the point-slope form of a linear equation

Since the slope of the desired line is the same as the slope of the given line, and the new line passes through the point \((-2, 2)\), we can use the point-slope form of a linear equation to write the equation of this line. The point-slope form of a linear equation is given by: \(y - y_1 = m(x - x_1)\) where \((x_1, y_1)\) is the point that the line passes through, and \(m\) is the slope of the line.
03

Plug in the given point and slope into the point-slope form equation

Plugging in the values \(x_1 = -2\), \(y_1 = 2\), and \(m = \frac{1}{2}\), we get: \(y - 2 = \frac{1}{2}(x - (-2))\)
04

Simplify the equation

Now, simplify the equation to get the final equation of the line: \(y - 2 = \frac{1}{2}(x + 2)\) To express the equation in slope-intercept form, distribute the slope to the terms in the parentheses and solve for y: \(y - 2 = \frac{1}{2}x + 1\) \(y = \frac{1}{2}x + 3\) So, the equation of the line that passes through the point \((-2, 2)\) and is parallel to the line \(2x - 4y - 8 = 0\) is: \(\boxed{y = \frac{1}{2}x + 3}\)

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!

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 the points lie on a straight line. $$ A(-1,7), B(2,-2), \text { and } C(5,-9) $$

Write the equation in the slopeintercept form and then find the slope and \(y\) -intercept of the corresponding line. $$ 2 x-3 y-9=0 $$

For each pair of supply-and-demand equations, where \(x\) represents the quantity demanded in units of 1000 and \(p\) is the unit price in dollars, find the equilibrium quantity and the equilibrium price. $$ 2 x+7 p-56=0 \text { and } 3 x-11 p+45=0 $$

For each demand equation, where \(x\) represents the quantity demanded in units of 1000 and \(p\) is the unit price in dollars, (a) sketch the demand curve and (b) determine the quantity demanded corresponding to the given unit price \(p\). $$ 2 x+3 p-18=0 ; p=4 $$

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If \(p=m x+b\) is a linear demand curve, then it is generally true that \(m<0\).
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Geometry

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.