/*! 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 9 Graph. List the slope and \(y\) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 9

Graph. List the slope and \(y\) -intercept. $$y=-2 x$$

Short Answer

Expert verified
Slope: -2, Y-intercept: 0.

Step by step solution

01

- Identify the Equation Format

The given equation is in the form of a straight line equation, which is generally represented as \(y = mx + b\) where \(m\) is the slope and \(b\) is the \(y\)-intercept.
02

- Determine the Slope

Compare the given equation \(y = -2x\) with the general form \(y = mx + b\). Here, \(m = -2\). Therefore, the slope is \(-2\).
03

- Determine the Y-Intercept

In the equation \(y = -2x\), the constant term \(b\) represents the \(y\)-intercept. Since there is no constant term present, the \(y\)-intercept is \(0\).
04

- Summarize the Solution

The slope of the line is \(-2\) and the \(y\)-intercept is \(0\).

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
The slope of a line is a measure of how steep the line is. It tells us how much the y-value changes for a unit increase in the x-value. The general form of a linear equation is represented as

\( y = mx + b \), where \( m \) stands for the slope.
In our given equation, \( y = -2x \), we can determine the slope by comparing it to the general form. Here, \( m = -2 \), which means the slope is \( -2 \).
If the slope is negative, like in this example, it indicates that the line is decreasing, or going downwards from left to right. A positive slope means the line is increasing, or going upwards.

Key Points:
  • The slope \( m \) in the equation \( y = mx + b \) indicates steepness and direction.
  • Negative slope (-2 in our case) shows a downward trend.
  • Positive slope shows an upward trend.
y-intercept
The y-intercept of a line is the point where the line crosses the y-axis. It's the value of y when x is zero. In the general equation \( y = mx + b \), the term \( b \) represents the y-intercept.

For our equation, \( y = -2x \), there is no constant term, meaning our equation can be written as \( y = -2x + 0 \). This indicates that the y-intercept \( b \) is \( 0 \).

Key Points:
  • The y-intercept \( b \) in the equation \( y = mx + b \) is where the line crosses the y-axis.
  • If there is no constant term, the y-intercept is 0.
  • In our equation, the y-intercept is 0.
graphing
Graphing a linear equation like \( y = -2x \) involves plotting the y-intercept and using the slope to determine the direction of the line.
First, plot the y-intercept (0,0) on the graph since it indicates where the line crosses the y-axis.
Next, use the slope to determine the next point. The slope of \( -2 \) means that for each step to the right (positive x direction), the line goes down by 2 units.

For example:
  • Starting at (0,0), move one unit to the right to (1,0)
  • Then, from (1,0), move down 2 units to (1,-2)

Repeat this step to draw a straight line through all points. Remember:
  • Mark the y-intercept first.
  • Use the slope to find additional points.
  • Draw a straight line through these points.

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

Life science: pollution control. Pollution control has become a very important concern in all countries. If controls are not put in place, it has been predicted that the function \(P=1000 t^{5 / 4}+14,000.\) will describe the average pollution, in particles of pollution per cubic centimeter, in most cities at time \(t,\) in years, where \(t=0\) corresponds to 1970 and \(t=35\) corresponds to 2005. a) Predict the pollution in 2005, 2008, and 2014. b) Graph the function over the interval \([0,50]\).

The amount of money, \(A(t),\) in a savings account that pays \(6 \%\) interest, compounded quarterly for \(t\) years, with an initial investment of \(P\) dollars, is given by $$ A(t)=P\left(1+\frac{0.06}{4}\right)^{4 t} $$ If \(\$ 800\) is invested at \(6 \%,\) compounded quarterly, how much will the investment be worth after 3 yr?

In 2000 the percentage of 18 - to 29 -year-olds who used the Internet was \(72 \%\). In 2009 , that percentage had risen to \(92 \%\) a) Use the year as the \(x\) -coordinate and the percentage as the \(y\) -coordinate. Find the equation of the line that contains the data points. b) Use the equation in part (a) to estimate the percentage of Internet users in 2010 . c) Use the equation in part (a) to estimate the year in which the percentage of Internet users will reach \(100 \%\) d) Explain why a linear equation cannot be used for years after the year found in part(c).

Give an example of a function for which the number 3 is not in the domain, and explain why it is not.

(See Exercise 68.) A business tenant spends 40 dollars per square foot on improvements to a \(25,000-\mathrm{ft}^{2}\) office space. Under IRS guidelines for straightline depreciation, these improvements will depreciate completely- that is, have zero salvage value-after 39 yr. Find the depreciated value of the improvements after 10 yr.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Decision 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.