Explanation:
The equation x = 0 represents a vertical line passing through the point (0, 0) on the coordinate plane. Let's break down the explanation into different sections:

Understanding the equation:
The equation x = 0 can be interpreted as "the value of x is always 0." This means that no matter what value y takes, x will always be 0. In other words, the line represented by this equation has all its points with x-coordinate equal to 0.

Graphical representation:
To graph the equation x = 0, we plot all the points on the coordinate plane where the x-coordinate is 0. Since only the x-coordinate is fixed at 0, the y-coordinate can vary. Therefore, all the points on this line will have the form (0, y), where y can be any real number.

Visualization:
If we imagine the coordinate plane, the equation x = 0 represents a vertical line passing through the origin (0, 0). This line is parallel to the y-axis because it is vertical and does not intersect or touch the y-axis at any point. It extends infinitely in both the positive and negative y-directions.

Relation to answer options:
Now let's relate this to the answer options:
a) The x-axis is a horizontal line and not parallel to the given equation, so it is not the correct answer.
b) A line parallel to the x-axis would have an equation in the form y = k, where k is a constant. Since the given equation does not have y, it is not parallel to the x-axis.
c) The equation x = 0 represents a line parallel to the y-axis, which means it is the correct answer.
d) A line parallel to the y-axis would have an equation in the form x = k, where k is a constant. The given equation matches this form, so it is parallel to the y-axis.
Therefore, the correct answer is option 'c', representing a line parallel to the y-axis.