How can I find the equation of a line that passes through the point (3, 6) with an undefined slope?

To find the equation of a line that passes through a specific point and has an undefined slope, we first need to understand what an undefined slope signifies. In mathematics, an undefined slope occurs when the line is vertical. This means that the x-coordinate of any point on the line remains constant, while the y-coordinate can vary.

Given the point (3, 6) and an undefined slope, we can determine the equation of the line as follows:

1. Identify the x-coordinate from the given point: In this case, the x-coordinate is 3.
2. Since the slope is undefined, the equation of the line will be of the form:

x = a

3. Here, ‘a’ is the constant value of the x-coordinate, which is 3.

Thus, the equation of the line is:

x = 3

This equation represents a vertical line that passes through the point (3, 6) and extends infinitely in both the upward and downward directions along the y-axis.