How do you calculate the slope of a line between two points?

To calculate the slope of a line between two points, you need to understand that the slope represents the rate of change in the vertical direction (the rise) compared to the horizontal direction (the run). The correct formula for slope is derived from the coordinates of the two points on the line, which we can denote as (x1, y1) and (x2, y2).

Using the coordinates, the rise is calculated as the difference in the y-coordinates (y2 - y1), indicating how far up or down the line goes. The run is calculated as the difference in the x-coordinates (x2 - x1), indicating how far left or right the line extends. Therefore, the slope is defined as the change in y over the change in x, which is given by the formula:

[ \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{y2 - y1}{x2 - x1} ]

This formula captures the essence of how steep the line is, showing the ratio of vertical change to horizontal change between the two points. In this context, understanding that a positive slope indicates an upward trend, while a negative slope indicates a downward trend is