Equation of the line y=0 represents

• a. x-axis
• b. y-axis
• c. Both x-axis and y-axis
• d. Neither x-axis nor y-axis

The equation of the line \( y = 0 \) specifically represents the x-axis in a Cartesian coordinate system. To understand why this is the case, let’s break it down step by step.

Understanding the Cartesian Plane

The Cartesian plane consists of two axes: the x-axis (horizontal) and the y-axis (vertical). Each point on this plane is defined by an ordered pair \((x, y)\), where \(x\) indicates the position along the x-axis and \(y\) indicates the position along the y-axis.

What Does \( y = 0 \) Mean?

When we look at the equation \( y = 0 \), it tells us that for any value of \( x \), the value of \( y \) is always zero. This means that no matter where you are on the x-axis, the height (or vertical position) is zero. Therefore, all points that satisfy this equation can be represented as \((x, 0)\), where \(x\) can be any real number.

Visualizing the x-axis

If you were to graph this equation, you would draw a horizontal line that runs along the x-axis. This line extends infinitely in both directions along the x-axis, confirming that it is indeed the x-axis itself. Here’s a simple way to visualize it:

All these points lie on the line where \( y = 0 \), which is the x-axis.

Clarifying the Options

Now, let’s analyze the options provided:

• a. x-axis - This is correct, as explained.
• b. y-axis - This is incorrect; the y-axis is represented by \( x = 0 \).
• c. Both x-axis and y-axis - This is incorrect; each axis has its own distinct equation.
• d. Neither x-axis nor y-axis - This is also incorrect, as we have established that \( y = 0 \) is indeed the x-axis.

Final Thoughts

In summary, the equation \( y = 0 \) exclusively represents the x-axis. Understanding the relationship between equations and their graphical representations is crucial in mathematics, as it helps in visualizing and solving problems effectively.