/*! 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 97 Explain how to use the general f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 97

Explain how to use the general form of a line's equation to find the line's slope and \(y\) -intercept.

Short Answer

Expert verified
One can find the slope and y-intercept by rearranging the general form \(Ax + By = C\) into slope-intercept form \(y = \frac{C}{B} - \frac{A}{B}x\). The slope will be \(-\frac{A}{B}\) and the y-intercept will be \(\frac{C}{B}\).

Step by step solution

01

Rearrange equation

The first step is to change the general form of the line's equation into the slope-intercept form. To do that, start from the general form of the line's equation, which is \(Ax + By = C\). Rearrange it to find \(y\) in terms of \(x\), which will yield the following: \(y = \frac{C}{B} - \frac{A}{B}x\).
02

Identify slope

Now that the equation of the line is in slope-intercept form, the coefficient of \(x\) in the equation, which is \(-\frac{A}{B}\), is the slope of the line.
03

Identify y-intercept

In the slope-intercept form of the line's equation, the constant term is the y-intercept, i.e., the value of \(y\) when \(x = 0\). So, \(\frac{C}{B}\) is the y-intercept of the line in this case.

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

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ x^{2}+y^{2}=16 $$

write the standard form of the equation of the circle with the given center and radius. $$ \text { Center }(-3,5), r=3 $$

If a function is defined by an equation, explain how to find its domain.

Will help you prepare for the material covered in the next section. Solve for \(y: \quad x=\frac{5}{y}+4\).

Does \((x-3)^{2}+(y-5)^{2}=-25\) represent the equation of a circle? What sort of set is the graph of this equation?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.