/*! 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 19 Find the \(x\) - and \(y\) -inte... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 19

Find the \(x\) - and \(y\) -intercepts. Then graph each equation. $$ y=5 $$

Short Answer

Expert verified
The y-intercept is (0, 5). There is no x-intercept.

Step by step solution

01

Identify the equation type

The equation given is a horizontal line, as it's in the form of y = b.
02

Find the y-intercept

Since the equation is y = 5, the y-intercept is the value of y when x=0, which is 5. Hence, the y-intercept is at (0, 5).
03

Find the x-intercept

To find the x-intercept, set y to 0 and solve for x. However, y = 5 never equals 0, so there is no x-intercept for this equation.
04

Graph the equation

Draw a horizontal line that crosses the y-axis at y=5. This line extends infinitely in both the positive and negative directions on the x-axis.

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 Equations
When you graph equations, you visually represent the relationship between variables on a coordinate plane. For the equation given, which is a simple equation of the form \(y = b\), we often see a straight line. This type of equation graphically shows how the value of y remains consistent, no matter what value x holds.
Horizontal Line
A horizontal line represents a situation where the value of y is constant. No upward or downward movement from the left to the right is displayed. For our given equation \(y = 5\), the graph will show a straight line parallel to the x-axis, intersecting the y-axis at y = 5.聽This means every point on this line will have a y-coordinate of 5. To graph a horizontal line:
  • Identify the y-intercept, which is the point where the line crosses the y-axis.
  • Draw a straight line across the graph, ensuring it is parallel to the x-axis and intersects the y-axis at y=5.
Intercepts
Intercepts are points where a line crosses the axes. For the equation \(y = 5\):
  • y-intercept: At x=0, the y-value is 5. Therefore, the y-intercept is at (0, 5).
  • x-intercept: For the x-intercept, we need to set y to 0. However, in \(y = 5\), y is always 5 and never 0. Thus, there is no x-intercept for this horizontal line.
To determine intercepts in general:
  • For the y-intercept, set x=0 and solve for y.
  • For the x-intercept, set y=0 and solve for x.
Identifying intercepts helps in sketching the graph accurately, providing crucial points where the line intersects the axes.

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

In 2010 , worldwide shipments of desktop computers totaled 157 million units. In 2016 , 103 million units were shipped. Find and interpret the average rate of change in worldwide shipments of desktop computers per year. (Data from IDC.)

Graph each line passing through the given point and having the given slope $$ (-3,1) ; \text { undefined slope } $$

In 2017 , the average Facebook user in the United States spent 693 more minutes per month using Facebook than the average Instagram user spent using Instagram. The average Instagram user spent 36 fewer minutes per month using Instagram than the average Snapchat user spent using Snapchat. The total amount of time that average users of each social network spent per month using their respective networks was 1347 min. How much time did the average user spend on each social network?

Graph each line passing through the given point and having the given slope $$ (5,3) ; m=0 $$

Determine whether each pair of lines is parallel, perpendicular, or neither $$ 3 x=y \text { and } 2 y-6 x=5 $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision 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.