/*! 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 28 Find the slope and y-intercept (... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 28

Find the slope and y-intercept (if possible) of the equation of the line. $$ 2 x+y=40 $$

Short Answer

Expert verified
The slope (m) of the line is -2 and the y-intercept (c) is 40.

Step by step solution

01

Rewrite the equation

To rewrite the equation into slope-intercept form, subtract 2x from both sides. This gives you \( y = -2x+40 \).
02

Identify the slope

The coefficient of x in the equation \( y = -2x+40 \) is -2. This is the slope (m).
03

Identify the y-intercept

The constant term in the formula, +40, represents the y-intercept (c) of the line. This is the point where the line crosses the y-axis.

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 is a mathematical expression that describes all points on a line in a coordinate plane. A common form of such an equation is known as the slope-intercept form, written as \(y = mx + c\). In this expression, \(m\) represents the slope of the line, and \(c\) is the y-intercept. To convert an equation into this form, we often manipulate it algebraically. For instance, if given \(2x + y = 40\), we reorganize it to separate \(y\). In this case, we subtract \(2x\) from both sides to obtain \(y = -2x + 40\).
  • This standardized form of the equation helps quickly identify key features of the line, such as its slope and where it crosses the y-axis.
  • It provides a direct correlation to the graph, aiding visual understanding.
Slope
The slope of a line is a measure of its steepness or inclination. In the slope-intercept form equation \(y = mx + c\), the term \(m\) represents the slope. It tells us how much the \(y\)-value changes for a given increment in the \(x\)-value. For example, in our equation \(y = -2x + 40\), the slope \(m\) is -2.
  • A positive slope means as \(x\) increases, \(y\) increases, hence the line goes upwards.
  • A negative slope, like -2 in our example, means as \(x\) increases, \(y\) decreases, so the line slopes downwards.
  • If the slope is zero, the line is horizontal.
Knowing the slope allows you to predict how a line will behave without having to draw it.
Y-intercept
The y-intercept is the point where a line crosses the y-axis of a graph. In the equation \(y = mx + c\), the \(c\) term represents this intercept. This tells you the value of \(y\) when \(x\) is 0.In our given equation \(y = -2x + 40\), the y-intercept is 40.
  • This means the line crosses the y-axis at \( (0, 40) \).
  • It serves as a starting point to draw the graph, setting where the line begins on the y-axis.
Understanding where your line intersects the y-axis is crucial for quickly sketching and interpreting the line's graph.

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

Complete the table and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. \(\lim _{x \rightarrow 0^{+}} \frac{\frac{1}{2+x}-\frac{1}{2}}{2 x}\) \(\begin{array}{|c|c|c|c|c|c|}\hline x & {0.5} & {0.1} & {0.01} & {0.001} & {0} \\\ \hline f(x) & {} & {} & {} & {} & {?}\\\ \hline\end{array}\)

Find the limit (if it exists). \(\lim _{x \rightarrow 2} \frac{2-x}{x^{2}-4}\)

Find the limit. \(\lim _{x \rightarrow 2} \frac{\frac{1}{x+2}-\frac{1}{2}}{x}\)

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. \(\lim _{x \rightarrow 1^{+}} \frac{5}{1-x}\)

Find the limit. \(\lim _{x \rightarrow 3} \frac{\sqrt{x+1}}{x-4}\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics 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.