A line with a slope of $0$ is a horizontal line, which means it has the same $y$-value for all $x$-values along the line. Since the line passes through the point $(3, -5)$, the $y$-value for every point on this line must be $-5$.

Thus, the equation of the line is: $y = -5$

The correct choice is (c) $y + 5 = 0$, which simplifies to $y = -5$.

Summary:

The correct answer is:

• (c) $y + 5 = 0$

Would you like further details on this concept or have any questions?

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Here are some related questions to explore further:

1. What is the general equation of a line with a slope of $0$?
2. How do you find the equation of a vertical line passing through a point?
3. How would the equation change if the slope were undefined?
4. What would the equation be if the slope were $1$ instead?
5. How do you convert a point-slope form equation into slope-intercept form?

Tip: Horizontal lines always have equations of the form $y = \text{constant}$, where the constant is the $y$-coordinate of any point on the line.