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Chapter 3: Problem 34

What is the equation of the \(x\) -axis? The equation of the \(y\) -axis?

Short Answer

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

Step by step solution

01

Identify the equation of the x-axis

The x-axis is a horizontal line where the value of y is always 0. Therefore, any point on the x-axis can be represented as \( (x, 0) \). The equation that satisfies this relationship is \( y = 0 \).
02

Identify the equation of the y-axis

The y-axis is a vertical line where the value of x is always 0. Therefore, any point on the y-axis can be represented as \( (0, y) \). The equation that satisfies this relationship is \( x = 0 \).

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Key Concepts

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

x-axis equation
The equation of the x-axis describes a horizontal line on a coordinate system. In this system, the value of the y-coordinate is always 0, while the x-coordinate can be any real number. Therefore, any point on the x-axis can be expressed in the form \( (x, 0) \).
This characteristic gives rise to the equation \( y = 0 \).

Understanding the x-axis is fundamental as it provides a reference line from which we measure the positions of points in a Cartesian coordinate system.
y-axis equation
Conversely, the equation of the y-axis describes a vertical line. In this case, the value of the x-coordinate is always 0, while the y-coordinate can be any real number. Thus, every point on the y-axis can be written as \( (0, y) \).
The equation that represents this line is \( x = 0 \).

The y-axis is equally important as the x-axis, offering another critical reference for locating points within a Cartesian coordinate system. Together, these axes form the backbone of the coordinate system.
coordinate system
A coordinate system is a method used to uniquely determine the position of a point or object in a space. The most common system is the Cartesian coordinate system, named after the mathematician Ren茅 Descartes. In two dimensions, it consists of two perpendicular lines or axes: the x-axis and the y-axis.

Key Features:
  • The x-axis runs horizontally.
  • The y-axis runs vertically.
  • Where they intersect is called the origin, represented as \( (0, 0) \).

Points are expressed as pairs of numbers \( (x, y) \), showing their horizontal and vertical distances from the origin. This system is essential for graphing equations and visualizing relationships between variables.

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Most popular questions from this chapter

Find an equation of the line passing through the given points. (a) Write the equation in standard form. (b) Write the equation in slope-intercept form if possible. $$(6,1)\( and \)(-2,5)$$

If a line has slope 0.2, then any line parallel to it has slope _____, and any line perpendicular to it has slope _____.

Find an equation of the line that satisfies the given conditions. (a) Write the equation in slope-intercept form. (b) Write the equation in standard form. Through \((4,1) ;\) parallel to \(2 x+5 y=10\)

Write each inequality or compound inequality using interval notation. See Sections 1.1 and 2.6. $$ -4 \leq x \leq 4 $$

Solve each problem. The upper deck at U.S. Cellular Field in Chicago has produced, among other complaints, displeasure with its steepness. It is 160 ft from home plate to the front of the upper deck and 250 ft from home plate to the back. The top of the upper deck is 63 ft above the bottom. What is its slope? (Consider the slope as a positive number here.)
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