/*! 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 43 Write the equation in the slopei... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 43

Write the equation in the slopeintercept form and then find the slope and \(y\) -intercept of the corresponding line. $$ 2 x+4 y=14 $$

Short Answer

Expert verified
The given equation \(2x + 4y = 14\) can be written in the slope-intercept form as \(y = -\frac{1}{2}x + \frac{7}{2}\). The slope of the corresponding line is m = \(-\frac{1}{2}\) and the y-intercept is b = \(\frac{7}{2}\).

Step by step solution

01

Write the given equation

First, let's write down the given equation: $$ 2x + 4y = 14 $$
02

Solve the equation for y

To put the equation into slope-intercept form (\(y = mx + b\)), we need to solve the equation for y. Subtract 2x from both sides of the equation: $$ 4y = -2x + 14 $$ Now, divide both sides by 4: $$ y = -\frac{1}{2}x + \frac{7}{2} $$
03

Identify the slope and y-intercept

Now that the equation is in slope-intercept form (\(y = -\frac{1}{2}x + \frac{7}{2}\)), we can easily identify the slope (m) and y-intercept (b). The coefficient of x (i.e., the number multiplied by x) is the slope, and the constant term is the y-intercept. In this case, we have: Slope (m): \(-\frac{1}{2}\) Y-intercept (b): \(\frac{7}{2}\)
04

Write the final answer

The given equation \(2x + 4y = 14\) can be written in the slope-intercept form as \(y = -\frac{1}{2}x + \frac{7}{2}\). The slope of the corresponding line is m = \(-\frac{1}{2}\) and the y-intercept is b = \(\frac{7}{2}\).

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!

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

Find an equation of the line that passes through the given points. $$ (-1,-2) \text { and }(3,-4) $$

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. Suppose the slope of a line \(L\) is \(-\frac{1}{2}\) and \(P\) is a given point on \(L\). If \(Q\) is the point on \(L\) lying 4 units to the left of \(P\), then \(Q\) is situated 2 units above \(P\).

The United States is not building many nuclear plants, but the ones it has are running at nearly full capacity. The output (as a percent of total capacity) of nuclear plants is described by the equation $$ y=1.9467 t+70.082 $$ where \(t\) is measured in years, with \(t=0\) corresponding to the beginning of 1990 . a. Sketch the line with the given equation. b. What are the slope and the \(y\) -intercept of the line found in part (a)? c. Give an interpretation of the slope and the \(y\) -intercept of the line found in part (a). d. If the utilization of nuclear power continues to grow at the same rate and the total capacity of nuclear plants in the United States remains constant, by what year can the plants be expected to be generating at maximum capacity?

The line with equation \(A x+B y+C=0(B \neq 0)\) and the line with equation \(a x+b y+c=0(b \neq 0)\) are parallel if \(A b-a B=0 .\)

Use the results of Exercise 63 to find an equation of a line with the \(x\) - and \(y\) -intercepts. $$ x \text { -intercept } 4 ; y \text { -intercept }-\frac{1}{2} $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics 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.