/*! 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 6 Use the slope-intercept form to ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 6

Use the slope-intercept form to graph each equation. $$ y=-6 x $$

Short Answer

Expert verified
Plot the points (0,0) and (1,-6). Draw the line through these points for the graph of the equation.

Step by step solution

01

Identify the Components

The equation is in the slope-intercept form, which is written as \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In the given equation, \( y = -6x \), the slope \( m = -6 \) and the y-intercept \( b = 0 \).
02

Plot the Y-Intercept

Start by plotting the y-intercept on the graph. Since \( b = 0 \), the y-intercept is at the origin \((0,0)\). Place a point at \( (0,0) \) on the graph.
03

Use the Slope to Determine Another Point

The slope \( m = -6 \) can be expressed as a fraction \( -6/1 \), meaning from the y-intercept, you move down 6 units (because it's negative) and 1 unit to the right. Start from \((0,0)\), move to \((1,-6)\). Plot this second point.
04

Draw the Line

With the two points \((0,0)\) and \((1,-6)\) plotted on the graph, draw a straight line through them. This line represents the equation \( y = -6x \). Extend the line across the graph to clearly show the direction and slope.

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.

Graphing Linear Equations
Graphing linear equations is a fundamental concept in algebra. It involves plotting points on a graph to create a straight line. The most common method is using the slope-intercept form, which is expressed as \( y = mx + b \), where \( m \) represents the slope and \( b \) the y-intercept of the line.
  • The equation helps determine the direction and steepness of the line.
  • Each point on the graph reflects a solution to the equation.
      • To graph an equation, you only need a few steps:
      • Identify the slope and y-intercept from the equation.
      • Plot the y-intercept on the y-axis.
      • Use the slope to find another point using rise over run.
      • Draw the line through these points.
      This ensures a precise graph that visually represents the relationship described by the equation.
Slope of a Line
The slope of a line, represented by \( m \) in the slope-intercept form, measures the steepness and direction of the line. It is calculated as the change in the \( y \) values (vertical) over the change in \( x \) values (horizontal), commonly called "rise over run."
  • If the slope is positive, the line rises as it moves from left to right.
  • If the slope is negative, the line falls as it moves from left to right.
  • A slope of zero indicates a horizontal line.
  • An undefined slope means a vertical line.
For example, in the equation \( y = -6x \), the slope is -6. This means for every 1 unit you move to the right, the line moves down 6 units. This steep negative slope results in a downward-sloping line that is quite steep. By understanding the slope, we can predict the behavior of the line without even graphing it.
Y-Intercept
The y-intercept is the point where the line crosses the y-axis. In the slope-intercept form \( y = mx + b \), the \( b \) value indicates the y-intercept. This is the starting point of the line when \( x \) is 0. For the equation \( y = -6x \), the y-intercept \( b = 0 \). This tells us the line goes through the origin \((0,0)\). Knowing the y-intercept is crucial:
  • It gives the location to start plotting on a graph.
  • It shows where to initially place the line.
Once the y-intercept is plotted, the slope helps continue the line across the graph. The y-intercept's value provides an anchor that fixes the position of the line on the graph, making it easier to visualize the full linear equation.

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

It's the end of the budgeting period for Dennis Fernandes, and he has \(\$ 500\) left in his budget for car rental expenses. He plans to spend this budget on a sales trip throughout southern Texas. He will rent a car that costs \(\$ 30\) per day and \(\$ 0.15\) per mile and he can spend no more than \(\$ 500\). a. Write an inequality describing this situation. Let \(x=\) number of days and let \(y=\) number of miles. b. Graph this inequality below. C. Why is the grid showing quadrant I only?

Graph each inequality. $$ x-y \leq 6 $$

Assume each exercise describes a linear relationship. Write the equations in slope-intercept form. In 2000 , crude oil field production in the United States was 2130 thousand barrels. In \(2007,\) U.S. crude oil field production dropped to 1850 thousand barrels. (Source: Energy Information Administration) a. Write two ordered pairs of the form (years after 2000, crude oil production). b. Assume the relationship between years after 2000 and crude oil production is linear over this period. Use the ordered pairs from part (a) to write an equation of the line relating years after 2000 to crude oil production. c. Use the linear equation from part (b) to estimate crude oil production in the United States in 2010 , if this trend were to continue.

Find an equation of each line described. Write each equation in slope- intercept form when possible. Through \((1,-5),\) parallel to the \(y\) -axis

Write an ordered pair for each point described. Find the area of the rectangle whose vertices are the points with coordinates \((5,2),(5,-6),(0,-6),\) and (0,2) .
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.