/*! 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 27 Find the \(x\) -intercept and th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 27

Find the \(x\) -intercept and the \(y\) -intercept for the graph of each equation. $$ y=2.5 $$

Short Answer

Expert verified
The \(y\)-intercept is \( (0, 2.5) \). There is no \(x\)-intercept.

Step by step solution

01

Identify equation

The given equation is a horizontal line: \(y = 2.5\). This means that for any value of \(x\), the value of \(y\) will always be 2.5.
02

Find y-intercept

To find the \(y\)-intercept, set \(x = 0\). \(y = 2.5\) when \(x = 0\). Thus, the \(y\)-intercept is \( (0, 2.5) \).
03

Find x-intercept

To find the \(x\)-intercept, set \(y = 0\). Since the equation \(y = 2.5\) does not satisfy this condition, there is no \(x\)-intercept.

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.

x-intercept
The x-intercept of a graph is the point where the graph crosses the x-axis. To find this intercept, we set the value of y to 0 and solve for x. This essentially gives the coordinate (x,0).
However, in the given equation, y = 2.5, you can see that no matter what value x takes, y is always 2.5. Therefore, it will never touch or cross the x-axis, which means there is no x-intercept for this equation.
y-intercept
The y-intercept is the point where the graph crosses the y-axis. To find the y-intercept, we set the value of x to 0 and solve for y, which provides us the coordinate (0,y).
In the equation y = 2.5, we set x = 0. Calculating this, we find y = 2.5. Thus, the y-intercept for this graph is (0, 2.5).
This tells us that the graph touches the y-axis at the point (0, 2.5).
horizontal line
A horizontal line has the same y-value for every x-value. It is visually represented as a straight line running left to right parallel to the x-axis.
For the equation y = 2.5, this means that the line is always at the height of 2.5 above the x-axis, regardless of the x-value.
Key features of a horizontal line include:
  • It has no slope (slope = 0).
  • It has no x-intercept because it never crosses the x-axis.
  • It has a constant y-value for all points on the line.
This makes horizontal lines unique and relatively simple to understand.

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

For each pair of equations, give the slopes of the lines and then determine whether the two lines are parallel, perpendicular, or neither. See Example \(6 .\) $$ \begin{aligned} &2 x+5 y=4\\\ &4 x+10 y=1 \end{aligned} $$

Plot and label each point in a rectangular coordinate system. $$ \left(-\frac{3}{2},-4\right) $$

A calculator can be thought of as a function machine. We input a number value (from the domain), and then, by pressing the appropriate key, we obtain an output value (from the range). Use your calculator, follow the directions, and then answer each question. Enter the value \(-8\) and then activate the squaring function, using the key labeled \(x^{2}\). A. What is the domain value here? B. What range value is obtained?

Describe what the graph of each linear equation will look like in the coordinate plane. (Hint: Rewrite the equation if necessary so that it is in a more recognizable form.) $$ 5 y=-15 $$

Find each quotient. $$ \frac{5-(-7)}{-4-(-1)} $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Decision 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.