Final answer:
Slope is the ratio of the vertical change to the horizontal change between two points on a graph, representing rise over run, and is crucial in diverse contexts such as calculating acceleration or average velocity.
Step-by-step explanation:
Slope is the ratio of the vertical change in coordinates, called the (rise/run), to the horizontal change in coordinates, called the (run). In mathematical terms, the slope or gradient of a line on a graph describes how steep the line is. To calculate the slope, one must divide the difference in the y-value (rise) by the difference in the x-value (run) between two points on the line.
For instance, in a physical context like a velocity versus time graph, the slope represents the acceleration, where rise equals the change in velocity and run equals the change in time. Similarly, the slope of a graph plotting displacement (x) against time (t) gives the average velocity.