What is the equation of the x axis?
Understand the Problem
The question is asking for the mathematical equation that represents the x-axis on a Cartesian coordinate system. The x-axis is the horizontal line where the y-coordinate is always zero.
Answer
The equation for the x-axis is \(y = 0\).
Answer for screen readers
The mathematical equation that represents the x-axis is (y = 0).
Steps to Solve
- Identify the characteristics of the x-axis
The x-axis is defined as the set of all points where the y-coordinate is equal to zero. This means that for any point on the x-axis, the value of (y) will always be (0).
- Express the definition in equation form
To represent this mathematically, we can denote the relationship between (x) and (y). Since the y-coordinate is always zero on the x-axis, we can write the following equation:
$$ y = 0 $$
This indicates that no matter what value (x) takes, (y) will remain (0).
The mathematical equation that represents the x-axis is (y = 0).
More Information
The x-axis is a fundamental aspect of the Cartesian coordinate system, serving as a reference line for measuring vertical distances (y-coordinates). It divides the plane into positive and negative y-values and is often used as a basis for graphing functions.
Tips
- A common mistake is confusing the x-axis with the y-axis. The x-axis is horizontal and associated with (y = 0), while the y-axis is vertical and associated with (x = 0).