Final answer:
The equation of the line perpendicular to y-4=0 and passing through (-1, 6) is x=-1.
Step-by-step explanation:
To find the equation of the line perpendicular to y-4=0, we need to determine the slope of the given line. The given equation y-4=0 can be rewritten as y=4, which represents a horizontal line with a slope of 0. A line perpendicular to this has a slope that is the negative reciprocal of 0, which is undefined. Therefore, it is a vertical line.
A vertical line passing through the point (-1, 6) will have the equation x=-1, since the x-coordinate remains constant for all points on a vertical line. Therefore, the equation of the line perpendicular to y-4=0 and passing through (-1, 6) is x=-1.
The equation y - 4 = 0 represents a horizontal line with a slope of 0. A line perpendicular to this would need to have an undefined slope, which means it is a vertical line. The equation of a vertical line that passes through a specific point, such as (-1, 6), will be in the form of x = a, where a represents the x-coordinate of the point of intersection.
Therefore, the equation of the line perpendicular to y - 4 = 0 and passing through (-1, 6) is simply x = -1.