/*! 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 56 Use the y-intercept and slope to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 56

Use the y-intercept and slope to sketch the graph of each equation. $$6-y=0$$

Short Answer

Expert verified
The graph is a horizontal line crossing the y-axis at 6.

Step by step solution

01

Write the Equation in Slope-Intercept Form

First, rearrange the given equation to the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. The given equation is \( 6 - y = 0 \). Solve for \( y \) by adding \( y \) to both sides and subtracting 6 from both sides to get \( y = 6 \).
02

Identify the Slope and Y-intercept

In the equation \( y = 6 \), the slope \( m \) is 0 as there is no \( x \) term. The y-intercept \( b \) is 6. This means the line is horizontal and crosses the y-axis at 6.
03

Sketch the Graph

To sketch the graph, plot a horizontal line that passes through the point (0, 6) on the y-axis. Since the slope is 0, the line will remain horizontal with no inclination.

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.

Understanding the Y-Intercept
The y-intercept is where the line crosses the y-axis. In an equation of the form \(y = mx + b\), \(b\) is the y-intercept. This value indicates the point at which the line touches the y-axis, meaning it is where \(x = 0\). For the equation in the exercise, \(y = 6\), the y-intercept is 6. This tells us that the line passes through the point (0, 6) on the coordinate plane. It's important to understand how to identify the y-intercept as it helps you quickly place at least one point on your graph.
Defining the Slope
The slope, represented by \(m\) in the equation \(y = mx + b\), defines the steepness of the line. It tells us how much the y-value changes for a one-unit change in the x-value. A positive slope means the line rises as it moves from left to right, while a negative slope means it falls. In the equation \(y = 6\), there's no \(x\) term, implying that the slope \(m\) is 0. This zero slope indicates a horizontal line, emphasizing no change in y as x varies.
Exploring the Slope-Intercept Form
The slope-intercept form of a linear equation is \(y = mx + b\). Here, \(m\) is the slope, and \(b\) is the y-intercept. This format makes it easier to graph linear equations because you can directly read off the slope and y-intercept. Given \(y = mx + b\), you can:
  • Identify the y-intercept \(b\), where the line crosses the y-axis.
  • Determine the slope \(m\), which tells you how the line slants.
Using these two parameters helps in creating an accurate graph of the linear equation.
Characteristics of Horizontal Lines
A horizontal line has a slope \(m\) of 0. It runs parallel to the x-axis and does not rise or fall. Equations such as \(y = c\), where \(c\) is a constant, describe horizontal lines. For instance, in the given exercise, \(y = 6\) represents a horizontal line passing through \(y = 6\). In graphing a horizontal line:
  • Plot a point at (0, c) on the y-axis.
  • Draw a straight line through this point, parallel to the x-axis.
This method ensures clarity and accuracy in representing 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

The diameter of a circle has endpoints \((1,3)\) and \((3,9)\) Find the equation of the circle.

Solve each equation. $$\frac{2}{x-1}-\frac{3}{x+2}=\frac{8-x}{x^{2}+x-2}$$

Find an exact solution to each problem. If the solution is irrational, then find an approximate solution also. Find the radius of the circle \(x^{2}+y^{2}=3 y\)

Dana inserted eight coins, consisting of dimes and nickels, into a vending machine to purchase a Snickers bar for 55 cents. How many coins of each type did she use?

Find the distance between the points \((-3,5)\) and \((2,8)\) and the midpoint of the line segment joining the points.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

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.