Final answer:
The slope of a line perpendicular to a vertical line is zero because a vertical line has an undefined slope, and the perpendicular line to it must be a horizontal line, which has a slope of zero.
Step-by-step explanation:
The slope of a line perpendicular to a vertical line is zero. This is because a vertical line has an undefined slope, and the slope of a line perpendicular to it will be the negative reciprocal. However, since you cannot have a reciprocal of an undefined value, we base our answer on the concept that perpendicular lines have slopes that are negative reciprocals of each other. With a vertical line's slope being undefined (or thought of as infinitely steep), the perpendicular line must be perfectly horizontal, thus having a slope of zero.
To understand the concept of slope further, we can consider the equation of a straight line, which is typically written as y = mx + b, where m is the slope and b is the y-intercept. The slope m represents the ratio of the rise (change in y) to the run (change in x). For a horizontal line, there is no rise (rise = 0), which leads to a slope of zero since dividing zero by any number results in zero. This corresponds to a flat line on a graph, where for any change along the x-axis, there is no change along the y-axis.
Considering real-world implications, when describing physical situations, if we were to report that a road has a slope of zero, we'd be saying the road is perfectly flat, with no incline or decline.