Let's analyze the problem.

You are asked to find the equation of the line that contains the point $(3, -4)$ and has a slope of $0$. When the slope is $0$, the line is horizontal. A horizontal line has the form:

$y = c$

Since the point on the line is $(3, -4)$, the y-coordinate of all points on the line must be $-4$. Therefore, the equation of the line is:

$y = -4$

The correct answer is:

$y = -4$

Do you have any further questions or want more details?

Here are 5 related questions to further your understanding:

1. What is the equation of a vertical line passing through $(3, -4)$?
2. How would the equation change if the slope were not zero but instead $1$?
3. Can a line have both a slope of zero and pass through two different points with different $y$-coordinates?
4. How can we calculate the slope if two points on the line are given?
5. What does a slope of infinity represent for a line?

Tip: Horizontal lines always have the form $y = \text{constant}$, while vertical lines have the form $x = \text{constant}$.