A vertical line has _________ slope.
A vertical line has an undefined slope.
A vertical line does not have a slope. The slope is undefined for a vertical line.
A vertical line has an undefined slope. To understand why this is the case, it's important to first understand what slope represents.
Slope is a measure of how steep a line is. It tells us how much the line rises or falls for every unit of horizontal change. In mathematical terms, slope is defined as the change in the y-coordinate (vertical change) divided by the change in the x-coordinate (horizontal change) between two points on a line.
For a vertical line, the change in the x-coordinate is zero since the line is perfectly vertical and doesn't move horizontally. However, the y-coordinate can change in any direction without any restrictions. This means that you can have infinite values for y while x remains constant. When we try to calculate the ratio of the change in the y-coordinate to the change in the x-coordinate for a vertical line, we end up with a division by zero, which is undefined in mathematics.
Therefore, when dealing with a vertical line, it is more accurate to say that it has an undefined slope rather than assigning it a specific numerical value.