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Chapter 3: Problem 78

What is the equation that describes the \(y\) -axis?

Short Answer

Expert verified
The equation of the y-axis is x = 0.

Step by step solution

01

Understanding the y-axis

The y-axis is a vertical line on a Cartesian coordinate plane that crosses the origin at point (0, 0). Thus, any point on the y-axis has its x-coordinate equal to 0.
02

Formulating the y-axis equation

Since every point on the y-axis has an x-coordinate of 0, the general equation of the y-axis in the Cartesian coordinate system is expressed as x = 0.
03

Summarizing the equation

Thus, the equation that describes the y-axis remains consistent regardless of the y-coordinate, as the key feature is the x-coordinate being exactly zero, leading to the equation x = 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

y-axis
In the Cartesian coordinate system, the y-axis is one of two perpendicular lines that form the plane. Imagining a graph you often see in math classes, the y-axis is a vertical line that spans from top to bottom. It serves as a reference line for measuring vertical distances.

Key characteristics of the y-axis include:
  • It crosses the x-axis at the origin, which is the point (0, 0).
  • All points along the y-axis have an x-coordinate of 0.
  • The y-axis can extend infinitely in both the positive and negative directions.
The equation for the y-axis is quite simple: it is described by the equation \( x = 0 \). This is because, at any point on this line, the x-value does not change and remains zero regardless of any movement up or down on the y-axis.
x-coordinate
The x-coordinate is a fundamental part of locating a point in the Cartesian coordinate system. It tells you how far a point is along the horizontal direction, which is parallel to the x-axis.

To better understand the x-coordinate:
  • It determines the distance of a point from the y-axis.
  • A positive x-coordinate means the point is to the right of the y-axis, while a negative x-coordinate indicates a position to the left.
  • When a point lies exactly on the y-axis, its x-coordinate is 0, as seen in the equation \( x = 0 \) for the y-axis itself.
The x-coordinate is the first number in the ordered pair (x, y), where \'y\' represents the vertical position. Together, these coordinates map precisely where the point is on the plane.
origin (0, 0)
The origin is a special point on the Cartesian plane where the x-axis and y-axis intersect. It is denoted as (0, 0). This central point acts as the starting point for measuring the positions of all other points in the coordinate plane.

Important aspects of the origin include:
  • Both the x-coordinate and the y-coordinate are zero, which is why it's represented as (0, 0).
  • It divides the plane into four quadrants, which help classify the position of points based on the signs of their coordinates.
  • The origin serves as a pivotal reference for understanding the movement of points along the axes.
This point of intersection makes the origin a vital part of graphing, enabling you to measure any other point's distance in relation to this benchmark.

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Most popular questions from this chapter

Find at least five ordered pair solutions and graph. $$ x=-3 $$

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Graph using the slope and \(y\) -intercept. $$ y=-52 x+3 $$
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