/*! 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 5 Which coordinate of a \(y\) -int... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 5

Which coordinate of a \(y\) -intercept is \(0 ?\) (GRAPH CAN'T COPY)

Short Answer

Expert verified
The x-coordinate of a y-intercept is 0.

Step by step solution

01

Understanding Y-intercept

A y-intercept is a point where a line, curve, or surface intersects the y-axis of a graph. In the Cartesian coordinate system, it refers to the point where the line crosses the y-axis. This point is represented by a coordinate pair.
02

Recognizing the Y-intercept in the coordinate system

In a 2D Cartesian coordinate system, any point on the surface can be represented by a pair of coordinates (x, y). When a line or curve intersects the y-axis, this means that the x (horizonal) coordinate of the point equals 0, as the y-axis is vertically aligned in the middle of the coordinate system.
03

Determining the Y-intercept coordinate

On the y-axis, which is a vertical line in a Cartesian coordinate system, the x-coordinate of any point will always be 0, while the y-coordinate can be any real number. Hence, at the y-intercept, the x coordinate is 0.

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.

Cartesian coordinate system
The Cartesian coordinate system is a foundational element in mathematics used for plotting points on a two-dimensional plane. This system was developed by Ren茅 Descartes and provides a way to visually express mathematical relationships.
It consists of two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical). These two axes intersect at a point called the origin, which has the coordinate (0, 0).
  • The x-axis represents the horizontal component of a point on the graph.
  • The y-axis represents the vertical component.
Each point on the plane can be defined by a pair of numbers, (x, y), known as its coordinates. This system is crucial for graphing equations and analyzing geometric shapes, as it provides a clear way to visualize data by mapping numerical points onto a grid.
Coordinates
Coordinates are numerical values that define the location of a point in a space relative to a reference origin. In a two-dimensional space, such as a Cartesian coordinate system, each point is identified by a pair of coordinates (x, y).
  • The first number, x, represents the position along the horizontal axis.
  • The second number, y, indicates the position along the vertical axis.
In the context of a y-intercept, the x-coordinate is always 0. This is because the point lies directly on the y-axis. Understanding how to use and interpret coordinates is key in plotting points and understanding the spatial relationships on a graph. It allows for precise location mapping and is used in various fields such as engineering, physics, and computer graphics.
2D graphs
Two-dimensional graphs are a powerful tool for visualizing mathematical functions and relations. These graphs plot equations or points in a plane, showcasing how one variable is affected by another.
  • They show relationships between two sets of data.
  • They help in interpreting trends, disparities, and behaviors in a dataset.
In these graphs, the y-intercept is a notable feature. It marks the point where a graph or a line crosses the y-axis, thus showing the value of the function when the independent variable (x) equals zero. This point is expressed with coordinates (0, y).
2D graphs are commonly used in statistics, science, and business to illustrate complex relationships in a simple, easily understandable way.

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

Determine whether there is a line that contains all of the given points. If so, find the equation of the line. $$(-1,-5),(2,4),(0,2)$$

Evaluate a function. Given \(f(x)=5 x+1,\) find \(f(2)\).

Determine whether the line through \(P_{1}\) and \(P_{2}\) is parallel, perpendicular, or neither parallel nor perpendicular to the line through \(Q_{1}\) and \(Q_{2}\). $$P_{1}(1,-1), P_{2}(3,-2) ; Q_{1}(-4,1), Q_{2}(2,-5)$$

Evaluate a function. Given \(P(x)=\frac{4}{2 x+1},\) find \(P(-2)\).

A rescue helicopter is rushing at a constant speed of 150 mph to reach several people stranded in the ocean 11 mi away after their boat sank. The rescuers can determine how far from the victims they are by using the equation \(D=11-2.5 t,\) where \(D\) is the distance in miles and \(t\) is the time elapsed in minutes. Graph this equation for values of \(t\) from 0 to \(4 .\) The point \((3,3.5)\) is on the graph. Write a sentence that describes the meaning of this ordered pair.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

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.