How is 'slope' described in a linear function?

In the context of a linear function, slope is defined as the ratio of the rise (the change in the y-values) over the run (the change in the x-values) between any two points on a line. This ratio provides a measure of how steep the line is, indicating the rate at which y changes for a given change in x. A positive slope means that as x increases, y also increases, while a negative slope indicates that as x increases, y decreases. This concept is fundamental in understanding linear relationships in graphs and is crucial for interpreting the behavior of the function.

The other options describe different concepts that do not accurately represent the definition of slope in a linear function. For example, the total distance between two points does not take into account the direction of the line, while the average of all y-values does not relate to slope directly. Similarly, the maximum value of y pertains to the limits of the function rather than the rate of change that slope describes.