/*! 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 26 Rearrange each linear equation i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 26

Rearrange each linear equation into slope-intercept form, \(y=m x+b\). \(3 y-4 x-1=8 x-2 y\)

Short Answer

Expert verified
The equation in slope-intercept form is \(y = \frac{12}{5}x + \frac{1}{5}\).

Step by step solution

01

- Combine Like Terms

First, move all terms involving variables to one side of the equation. Begin by adding or subtracting the terms on both sides to combine like terms. Starting with the given equation: \(3y - 4x - 1 = 8x - 2y\)Add \(2y\) to both sides: \(3y + 2y - 4x - 1 = 8x\).So, we get: \(5y - 4x - 1 = 8x\).
02

- Isolate the y-Terms

Next, isolate the \( y \)-terms on one side of the equation: \(5y = 8x + 4x + 1\).Combine like terms on the right-hand side: \(5y = 12x + 1\).
03

- Solve for y

Now, divide each term by 5 to solve for \(y\): \(y = \frac{12x + 1}{5}\).Express the solution in slope-intercept form: \(y = \frac{12}{5}x + \frac{1}{5}\).

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.

linear equations
A linear equation is an equation that models a straight line when graphed on a coordinate plane. Linear equations have the general form: ax + by = c, where a, b, and c are constants. The idea is to find all pairs (x, y) that satisfy the equation. By rearranging these equations, we can better understand their properties, such as slope and y-intercept. This is particularly useful in real-world scenarios, for example, when calculating costs, distances, or predicting future events.
combining like terms
Combining like terms means simplifying an equation by summing or subtracting terms that have the same variable. For example, in the equation 3y - 4x - 1 = 8x - 2y, both 3y and -2y are like terms because they contain the variable 'y'.
To combine these, you add 2y to both sides, resulting in 3y + 2y - 4x - 1 = 8x.
Doing this helps in simplifying equations, making it easier to isolate a specific variable later on.
isolating variables
Isolating variables involves moving terms around to get the variable of interest by itself on one side of the equation. For instance, to isolate the y-term in our given equation: 5y - 4x - 1 = 8x, you would add 4x and 1 to both sides to get 5y = 8x + 4x + 1.
This ensures all y-terms are on one side, simplifying the equation further.
Isolating variables is a key step in solving linear and other types of equations, as it allows us to solve for specific variables.
solving for y
Solving for y means rearranging an equation to make y the subject. Once the y-terms are isolated, divide each term by the coefficient of y to find its value.
In the final step of our exercise: 5y = 12x + 1, divide both sides by 5 to get: y = (12/5)x + 1/5.
This gives you the slope-intercept form: y = mx + b, where m is the slope (12/5) and b is the y-intercept (1/5).
This standardized form makes it easy to identify key properties of the line and to graph it.

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

Write an equation of a line that is parallel to the given line. \(x=-2\)

Hector conjectured that when you subtract an even number from an odd number, the result is odd. He tried to prove his conjecture. Hector said, "According to my proof, an odd number minus an even number is always 1 . This isn't true. What did I do wrong?" a. What did Hector do wrong? b. Give a correct proof of Hector's conjecture.

In Exercises \(15-17\) , decide whether the conjecture is true or false. Try to give a convincing proof of the conjectures that are true. For false conjectures, give a counterexample. The square of every even number is a multiple of 4.

Evaluate each expression for the given values. $$ a^{d}+a b-b^{c} \text { for } a=-3, b=-2, c=3, \text { and } d=2 $$

Kiyoshi spent \(\$ 8\) at the farmer's market. She bought only mandarin oranges, which are \(\$ 0.40\) each, and nectarines, which are \(\$ 0.80\) each. a. Is the relationship between the number of mandarin oranges, m, and the number of nectarines, n, an inverse variation? Explain. b. Write an equation for the relationship between m and n.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.