/*! 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 29 Find the slope and y-intercept (... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 29

Find the slope and y-intercept (if possible) of the equation of the line. $$ 7 x+6 y=30 $$

Short Answer

Expert verified
The slope (m) of the line is -7/6 and the y-intercept (b) is 5.

Step by step solution

01

Rearrange the Equation

First step is to rearrange the equation into slope-intercept form y = mx + b. Start by subtracting 7x from both sides to isolate y: 6y = -7x + 30
02

Find the Slope

Next, divide every term in the equation by 6 to solve for y, which results in y = -7/6x + 5. Here the coefficient of x is -7/6, which is the slope of the line (m).
03

Find the y-intercept

After the step 2, the equation is now in the form y = -7/6x + 5. The constant term on the right-hand side is 5 which corresponds to the y-intercept (b).

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.

Equation of a line
The equation of a line in its general form usually looks something like this: \( Ax + By = C \). This represents a straight line on a graph. Each part of the equation has a specific role:
  • \( A \) and \( B \) are coefficients that help determine the slope of the line.
  • \( C \) is a constant that influences the position of the line.
This form is just one way to write the equation of a line. To better grasp other forms, let's look into how we can manipulate and rearrange these equations.
Slope-intercept form
The slope-intercept form of a line equation is very practical because it clearly displays the slope and y-intercept. This format is written as \( y = mx + b \). Here,
  • \( m \) represents the slope, showing how steep the line is.
  • \( b \) represents the y-intercept, which is the point where the line crosses the y-axis.
Using slope-intercept form, you can quickly identify these two crucial characteristics of a line. This form demonstrates how a change in \( x \) affects \( y \), making it particularly useful for graphing lind or understanding a line's behavior.
Rearranging equations
Rearranging equations is a powerful tool to convert complex equations into more understandable forms. Taking an equation like \( 7x + 6y = 30 \) and rearranging it to \( y = mx + b \) involves a few steps:
  • First, isolate the term with \( y \). In this case, move \( 7x \) to the other side, leading to \( 6y = -7x + 30 \).
  • Next, divide the entire equation by 6 to solve for \( y \), turning it into \( y = -\frac{7}{6}x + 5 \).
Through these steps, you now have the line in slope-intercept form. This makes identifying the slope and y-intercept straightforward. Rearranging equations enhances your ability to explore different properties of mathematical expressions with ease.

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 the limit (if it exists). \(\lim _{x \rightarrow-1} \frac{x^{3}-1}{x+1}\)

Use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. \(\lim _{x \rightarrow 1^{+}} \frac{5}{1-x}\)

use a graphing utility to graph the function. Then use the Horizontal Line Test to determine whether the function is one-to-one. If it is, find its inverse function. $$ g(t)=\frac{t+3}{1-t} $$

Describe the interval(s) on which the function is continuous. $$ f(x)=\frac{1}{2}\|2 x\| $$

Express the value of a real estate firm in terms of the number of acres of property owned. Each acre is valued at \(2500 and other company assets total \)750,000.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

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.