/*! 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 50 What is the common name given to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 50

What is the common name given to a line with slope 0 whose \(y\) -intercept is the origin?

Short Answer

Expert verified
The line is commonly known as the x-axis.

Step by step solution

01

Understand the Slope

The slope of a line indicates how steep the line is. A slope of 0 means that the line is horizontal, as there is no rise over run.
02

Identify the y-Intercept

The y-intercept of a line is the point where the line crosses the y-axis. Given that the y-intercept is at the origin, this point is (0, 0).
03

Combine Both Characteristics

Since the line has a slope of 0 (indicating it is horizontal) and it passes through the origin (0, 0), it is a special type of horizontal line.
04

Conclusion

A horizontal line that passes through the origin is commonly known as 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.

Slope
The slope of a line indicates how steep the line is. Mathematically, it is defined as the ratio between the change in the y-coordinate and the change in the x-coordinate. It is denoted by the letter \(m\). For a line, we use the formula:
\[ m = \frac{\Delta y}{\Delta x} \] Here, \( \Delta y \) is the difference in the y-values (rise), and \( \Delta x \) is the difference in the x-values (run). When a line has a slope of 0, the value of \( \Delta y \) is 0, meaning there is no vertical change. The line remains flat, forming a horizontal line. Such a line means that no matter how much the x value changes, the y value stays constant.
y-intercept
The y-intercept is the point where a line crosses the y-axis. This is where the x-coordinate is 0. For example, if you have the equation of a line in the form of \( y = mx + b \), \(b \) represents the y-intercept.
In our case, the exercise indicates that the y-intercept is at the origin. The origin is the point (0, 0) where both the x and y axes intersect. Therefore, if a line crosses the y-axis at (0, 0), it means that when \( x = 0 \), the value of \( y \) is also 0.
x-axis
The x-axis is a horizontal number line in the coordinate plane. It represents the set of all possible values of the variable \(x\). When a line is perfectly horizontal and passes through the origin (0, 0), it lies flat along the x-axis. Because the slope is 0, the equation of such a line can be written as
\( y = 0 \)
This equation indicates that for all values of \(x\), the value of \(y\) remains zero. The x-axis itself is the reference line where the y-coordinate is always 0.
Origin
The origin is a special point in the coordinate system. It is where the x-axis and the y-axis intersect, and it has coordinates (0, 0). The origin is often used as a starting reference for plotting points and lines on the Cartesian plane.
When we talk about a line that passes through the origin with a slope of 0, we mean that the line is horizontal and crosses (0, 0). Thus, the line coincides with the x-axis. This is because the point (0, 0) is crucial in identifying both the direction and position of the line.

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 function \(f,\) find \((a) f(2),(b) f(0),\) and \((c) f(-3) .\) See Example 5 $$ f(x)=x^{2}-x+2 $$

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

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.) $$ 2 x=4 y $$

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 \(6 .\) $$ \begin{aligned} &3 x-5 y=-1\\\ &5 x+3 y=2 \end{aligned} $$

Solve each problem. Suppose that it costs \(\$ 5000\) to start up a business selling snow cones. Furthermore, it costs \(\$ 0.50\) per cone in labor, ice, syrup, and overhead. Then the cost to make \(x\) snow cones is given by \(y\) dollars, where $$ y=0.50 x+5000 $$ Express each of the following as an ordered pair. (a) When 100 snow cones are made, the cost is \(\$ 5050\). (b) When the cost is \(\$ 6000\), the number of snow cones made is 2000 .
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.