Which formula is used to find the slope of a line?

The formula used to find the slope of a line is indeed encapsulated in several related expressions, making "all of the above" the comprehensive choice. Each option represents a way to conceptualize or calculate the slope, which is fundamentally a measure of how steep a line is.

The expression "slope = rise/run" captures the geometric interpretation of slope, indicating that it is the vertical change (rise) over the horizontal change (run) between two points on a line.

Similarly, "slope = change in x/change in y" is another way to express this concept, focusing on the changes in the respective coordinates. However, it’s crucial to note that for the slope formula to be valid, it should actually be "change in y/change in x", which emphasizes the output (y) changing relative to the input (x).

The formula "slope = (y2 - y1)/(x2 - x1)" explicitly uses the coordinates of two distinct points on the line, providing a tangible method for calculating the slope. It inherently reflects the "rise/run" concept while being derived from the coordinate points.

Thus, combining all these formulations, they represent the same fundamental idea of slope, just articulated in different mathematical expressions or contexts