A horizontal line has a constant $y$-value, which means its equation is of the form:

$y = c$

where $c$ is the $y$-coordinate of every point on the line. Since the line passes through the point $(4, 7)$, the $y$-value for all points on this line is $7$.

Thus, the equation of the horizontal line that passes through $(4, 7)$ is:

$y = 7$

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the equation of a vertical line passing through the point $(4, 7)$?
2. What is the slope of a horizontal line?
3. If another point $(5, 7)$ is on this line, does it satisfy the equation $y = 7$?
4. How would the equation change if the line passed through $(4, -3)$?
5. What is the distance between the points $(4, 7)$ and $(10, 7)$ on this line?

Tip: Horizontal lines always have a slope of 0 because there is no vertical change between any two points on the line.