/*! 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 8 Graph \(x-2 y=8\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 8

Graph \(x-2 y=8\)

Short Answer

Expert verified
The graph of the equation \(x-2y=8\) is a straight line with slope 0.5 and y-intercept -4.

Step by step solution

01

Rearrange the Equation

Rearrange the given equation \(x-2y=8\) to the form \(y=mx+c\) by isolating y. The resulted equation will be \(y=0.5x-4\). Hence, the slope m is 0.5 and y-intercept c is -4.
02

Compute Points

Choose any three values for x. For example x=0, x=2, and x=4. Substitute these values into the equation to get the corresponding y-values. (x=0, y=-4), (x=2, y=-3), and (x=4, y=-2). Hence, these three points (0,-4), (2,-3), and (4,-2) lie on the line.
03

Plot the Graph

Plot y-intercept (0,-4) on the y-axis and other points (2,-3), and (4,-2) on the Cartesian plane. Then draw a straight line passing through all the points, which is the graph of the equation \(x-2y=8\).

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-intercept Form
The slope-intercept form is an essential concept when working with linear equations. This form is represented as \(y = mx + b\), where:
  • \(m\) is the slope of the line. It indicates the steepness and direction of the line. A positive slope means the line is increasing, while a negative slope means it's decreasing.
  • \(b\) is the y-intercept. This is where the line crosses the y-axis, showing the starting point of the line on a graph.
To rewrite the equation \(x - 2y = 8\) in slope-intercept form, you solve for \(y\). Rearranging gives \(y = 0.5x - 4\). Hence, the slope \(m\) is 0.5, and the y-intercept \(b\) is -4. Understanding how to express an equation in this form makes it easier to sketch the graph.
Plotting Points
Plotting points accurately on a graph is crucial for representing equations visually. After finding the equation in slope-intercept form, determine specific points that lie on the line by selecting values for \(x\) and solving for \(y\).
For instance, with the equation \(y = 0.5x - 4\), you can choose several \(x\) values, such as 0, 2, and 4:
  • When \(x = 0\), \(y = -4\). So, the point is (0, -4).
  • When \(x = 2\), \(y = -3\). So, the point is (2, -3).
  • When \(x = 4\), \(y = -2\). So, the point is (4, -2).
Plot these calculated points on the graph, and ensure your plotted points lead to a straight line. This helps visualize the relationship between \(x\) and \(y\).
Cartesian Plane
The Cartesian plane, also known as the coordinate plane, is a two-dimensional plane divided by the x-axis and y-axis. This plane is essential for plotting and understanding linear equations.
  • The horizontal axis is called the x-axis.
  • The vertical axis is called the y-axis.
  • Where the axes intersect is called the origin, denoted as (0,0).
In this system, each point's location is determined by a pair of numerical coordinates: \(x\) and \(y\). In our example, when plotting the points (0, -4), (2, -3), and (4, -2), we place them accordingly on this plane. The Cartesian plane facilitates the visualization of the relationship by allowing you to draw the line through these points, representing the equation \(x - 2y = 8\).
Linear Graphs
Linear graphs are graphical representations of linear equations. These graphs show a straight line that extends infinitely in both directions.
The equation \(y = mx + b\) creates a linear graph with a clear slope \(m\) and a y-intercept \(b\). Here鈥檚 how to construct a linear graph:
  • First, convert the given equation into slope-intercept form if it's not already.
  • Next, determine and plot the y-intercept on the graph.
  • Plot additional points on the graph by selecting values for \(x\) and calculating \(y\).
  • Finally, connect these points with a straight line that extends across the plane.
The plotted line will show the relationship dictated by the equation, such as \(x - 2y = 8\), and helps in predicting values or understanding the equation's nature. Linear graphs are a simple yet powerful tool in mathematics, making complex relationships easy to comprehend.

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

Graph the line that passes through the given point and has the given slope. (2,3) and \(m=0\)

Solve for \(x\) and \(y\). \(y=3 x+4\) \(y=5 x-2\)

A female college student who is 60 inches tall weighs 100 pounds, and another female student who is 66 inches tall weighs 124 pounds. Assuming the relationship between the female students' weights and heights is linear, write an equation giving the relationship between heights and weights of female students, and use this relationship to predict the weight of a female student who is 70 inches tall.

Find an equation of the line whose x-intercept is 2 and y-intercept 3 .

The supply curve for a product is \(y=300 x+9000,\) and the demand curve is \(y=-100 x+14000\) where \(x\) represents the price and \(y\) the number of items. At what price will the supply equal demand, and how many items will be produced at that price?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

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.