/*! 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 4 Graph. $$ y=-2 $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 4

Graph. $$ y=-2 $$

Short Answer

Expert verified
The graph is a horizontal line at \(y = -2\).

Step by step solution

01

Identify the Type of Equation

The equation given is \(y = -2\), which means it represents a horizontal line on the Cartesian plane.
02

Understand the Slope of the Line

In the equation \(y = -2\), the line is horizontal, meaning the slope is \(m = 0\). This indicates that for every change in \(x\), \(y\) remains constant.
03

Determine the Position on the Graph

The line is positioned at \(y = -2\) across all values of \(x\). This means that no matter what \(x\) value you choose, the \(y\) value will always be \(-2\).
04

Draw the Graph

Plot a straight line horizontally across the graph at the \(y\)-value of \(-2\), ensuring it crosses the entire graph from left to right.

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 of a Line
When we talk about the slope of a line, we're discussing how steep the line is. This is represented by the letter \(m\) in the equation of a line, \(y = mx + b\). The slope tells us how much the \(y\) value changes for each change in \(x\).
For instance, if the slope \(m = 2\), it means that for every 1 unit increase in \(x\), \(y\) increases by 2 units.
  • A positive slope means the line goes up as you move from left to right.
  • A negative slope means the line goes down as you move from left to right.
  • A zero slope means the line is horizontal, and the \(y\) value doesn't change regardless of the \(x\) value.
In the case of the equation \(y = -2\), the slope \(m = 0\). This tells us that the line doesn't rise or fall; it remains flat across the graph.
Cartesian Plane
The Cartesian Plane is a two-dimensional space defined by two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). It helps us graph and visualize different math functions. Each point on this plane has a unique pair of coordinates, \((x, y)\).
Graphing involves plotting points or lines by using these coordinates. For example:
  • A point like \((3, 4)\) would be 3 units to the right on the x-axis and 4 units up on the y-axis.
  • To plot our line \(y = -2\), we mark all points where the y-coordinate is -2, such as \((0, -2)\), \((1, -2)\), \((2, -2)\), and so on.
The magic of the Cartesian Plane lies in how it enables us to visually interpret algebraic equations, making them easier to understand and analyze.
Equation of a Line
Understanding the equation of a line is central to graphing. The standard form of a line's equation is \(y = mx + b\), where:
  • \(m\) represents the slope of the line.
  • \(b\) is the y-intercept, which is where the line crosses the y-axis.
In the equation \(y = -2\), it might look different from the standard form, but it is still an equation of a line. Here, instead of \(mx\), we only have a constant \(b = -2\). This tells us:
  • The line is horizontal, as shown by the absence of an \(x\) term, indicating \(m = 0\).
  • The y-intercept is -2, meaning the line crosses the y-axis at \(y = -2\).
Such equations are simpler since the value of \(y\) is constant and helps depict horizontal lines on a 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

Pollution control has become an important concern worldwide. The function $$P(t)=12.85 t^{-0.077}$$ describes the average pollution, in micrograms per cubic meter of air, \(t\) years after 2000. (Source: epa.gov/ airtrends/pm.html) a) Predict the pollution in \(2015,2020,\) and 2025 . b) Graph the function over the interval [0,50] .

Rewrite each of the following as an equivalent expression with rational exponents. $$ \sqrt[3]{t^{6}} $$

Rewrite each of the following as an equivalent expression with rational exponents. $$ \sqrt[5]{a^{3}} $$

A large crane is being depreciated according to the model \(V(t)=900-60 t,\) where \(V(t)\) is in thousands of dollars and \(t\) is the number of years since \(2005 .\) If the crane is to be depreciated until its value is \(\$ 0,\) what is the domain of this model?

Rewrite each of the following as an equivalent expression using radical notation. $$ \left(x^{2}-3\right)^{-1 / 2} $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.