What is the slope of a line?

The slope of a line is fundamentally defined as a number that quantifies both the direction and steepness of the line. It represents the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. A positive slope indicates that the line rises as it moves from left to right, while a negative slope shows that the line falls. The steeper the line, the greater the absolute value of the slope. This concept is crucial in various fields such as mathematics, physics, and engineering, where understanding the relationship between two variables is essential.

The other options do not accurately capture the definition of slope. For instance, while a line’s length could be a related concept, it does not inform about the slope. The point where the line crosses the y-axis is referred to as the y-intercept, which is unrelated to the measurement of the slope. Additionally, the vertical distance between two points on the line alone does not provide the necessary context for understanding how steep or in which direction the line travels, thus failing to encapsulate the full definition of slope.