/*! 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 31 Graph each linear equation. Plot... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 31

Graph each linear equation. Plot four points for each line. $$x=2$$

Short Answer

Expert verified
The line is vertical at \(x = 2\). Plot points: (2, -2), (2, -1), (2, 0), (2, 1).

Step by step solution

01

Understand the Equation

The given equation is written as \(x = 2\). This is a vertical line where the value of x remains constant at 2, regardless of the value of y.
02

Choose Values for y

To plot points on this line, select different values for y. For simplicity, let's choose four values: \(y = -2, -1, 0, 1\).
03

Generate Points

For each chosen y value, use the equation to determine the corresponding x value. Since \(x = 2\) always, the points generated will be: \( (2, -2) \), \( (2, -1) \), \( (2, 0) \), and \( (2, 1) \).
04

Plot the Points

Plot the points \( (2, -2) \), \( (2, -1) \), \( (2, 0) \), and \( (2, 1) \) on the coordinate plane.
05

Draw the Line

Draw a straight line passing through all four points. This line represents the equation \(x = 2\). It is a vertical line crossing the x-axis at \(x = 2\).

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.

Vertical Lines
Vertical lines are a unique type of line on the coordinate plane. They are defined by the equation x = constant, where 'constant' is a specific number. A vertical line means that no matter what the y value is, the x value always remains the same. For instance, in the equation x = 2, the x value will always be 2, no matter the y value. This is why when you plot the points of a vertical line, all the points will have the same x coordinate. Vertical lines run parallel to the y-axis and have an undefined slope because you can't quantify a rise over run when there鈥檚 no horizontal movement.
Coordinate Plane
The coordinate plane is a two-dimensional surface on which we can plot points, lines, and curves. It is formed by the intersection of two straight lines: the x-axis (horizontal) and the y-axis (vertical). These axes divide the plane into four quadrants. Each point on the coordinate plane is identified by an ordered pair (x, y), where x indicates the horizontal position and y indicates the vertical position. The point where the axes intersect is called the origin, represented by the coordinates (0, 0). Understanding the structure of the coordinate plane is essential for graphing equations as it helps you accurately locate points and visualize algebraic relationships.
Plotting Points
Plotting points is the first step in graphing any equation. A point is determined by its coordinates, given as (x, y). To plot a point:
  • Start at the origin (0, 0).
  • Move horizontally to the x value.
  • From there, move vertically to the y value.
For example, to plot the point (2, -2):
  • Start at the origin.
  • Move 2 units to the right (positive x direction).
  • Then move 2 units down (negative y direction).
Repeat this for all points to be plotted. In the given exercise, for the line x = 2, you will plot points (2, -2), (2, -1), (2, 0), and (2, 1). Once all points are plotted, draw a line through them to represent the vertical line x = 2.

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

Explain the difference between a compound inequality using the word and and a compound inequality using the word or.

Graph each pair of lines in the same coordinate system using the slope and y-intercept. $$\begin{aligned}&y=x+3\\\&y=x+2\end{aligned}$$

Solve each problem. For a one-day car rental the X-press Car Company charges \(C\) dollars, where \(C\) is determined by the function \(C=0.26 m+42\) and \(m\) is the number of miles driven. a) What is the charge for a car driven 400 miles? b) Sketch a graph of the equation for \(m\) ranging from 0 to 1000

Find the equation of line l in each case and then write it in standard form with integral coefficients. Line \(l\) has \(x\) -intercept \((2,0)\) and \(y\) -intercept \((0,4)\).

Solve each problem. See Example 9. Heating water. The temperature of a cup of water is a linear function of the time that it is in the microwave. The temperature at 0 seconds is \(60^{\circ} \mathrm{F}\) and the temperature at 120 seconds is \(200^{\circ} \mathrm{F}\) a) Express the linear function in the form \(t=m s+b\) where \(t\) is the Fahrenheit temperature and \(s\) is the time in seconds. [Hint: Write the equation of the line through \((0,60) \text { and }(120,200) .]\) b) Use the linear function to determine the temperature at 30 seconds. c) Graph the linear function.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

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.