/*! 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 105 In the following exercises, grap... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 105

In the following exercises, graph each equation. $$ 4 x+y=2 $$

Short Answer

Expert verified
Convert the equation to y = -4x + 2, then plot (0, 2) and (1, -2), draw the line through these points.

Step by step solution

01

Identify the equation format

The given equation is in a standard linear form: y = mx + bHowever, the provided equation is not yet in this form: 4x + y = 2Let's convert it.
02

Rearrange the equation to slope-intercept form

Solve for y to put it into the form y = mx + b. Start by isolating y on one side of the equation. First, subtract 4x from both sides: 4x + y - 4x = 2 - 4xy = -4x + 2Now, the equation is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
03

Identify the slope and y-intercept

From the equation y = -4x + 2: The slope (m) is -4, and the y-intercept (b) is 2.
04

Find the y-intercept point on the graph

The y-intercept is the point where the graph crosses the y-axis. Since b = 2, plot the point (0, 2) on the y-axis.
05

Use the slope to find another point

The slope (m) of -4 means that for every 1 unit you move to the right on the x-axis (positive direction), you move 4 units down (negative direction) on the y-axis.From the y-intercept (0, 2), move 1 unit to the right to (1, 2), then 4 units down to (1, -2). Plot this point (1, -2).
06

Draw the line

Draw a straight line through the points (0, 2) and (1, -2). This line represents the graph of the equation y = -4x + 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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

slope-intercept form
The slope-intercept form of a linear equation is one of the most common and useful ways to express a line in algebra. It is written as: \( y = mx + b \). Here,
  • \

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

In the following exercises, graph each equation. $$ x=3 $$

In the following exercises, graph the vertical or horizontal lines. $$ y=-2 $$

In the following exercises, find the slope of each line. $$ y=-1 $$

In the following exercises, find the ordered pairs that are solutions to the given equation. \(5 x+y=10\) (a) \((5,1)\) (b) \((2,0)\) (c) \((4,-10)\)

In the following exercises, graph by plotting points. $$ \frac{1}{3} x+y=2 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Geometry

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.