Final answer:
The equation of the horizontal line that passes through (4,6) is y = 6, as the y-value remains constant along a horizontal line.
Step-by-step explanation:
The question asks to find the equation of the horizontal line that passes through the point (4,6). A horizontal line has a slope of zero, which means that no matter how much we move along the x-axis, the y-value remains constant. Therefore, the equation of any horizontal line can be written as y = k, where k is the y-coordinate of any point on the line. Since our line passes through the point (4,6), the y-value is 6. This means the equation of the horizontal line is y = 6.