The equation of the horizontal line that passes through the point $(-7, 1)$ is:

$y = 1$

This equation indicates that the $y$-coordinate is always $1$, regardless of the $x$-coordinate.

Would you like more details or have any other questions?

Here are five related questions you might consider:

1. What is the equation of a horizontal line that passes through the point $(2, -3)$?
2. How would the equation change if the point were $(-7, 5)$?
3. What is the equation of a horizontal line that passes through the origin $(0, 0)$?
4. Can a horizontal line ever intersect a vertical line?
5. How do you determine the distance between two horizontal lines?

Tip: The equation of a horizontal line is always in the form $y = \text{constant}$, where the constant is the $y$-coordinate of any point on the line.