Which formula represents the slope of a line in mathematics?

The slope of a line in mathematics is defined as the ratio of the rise (the change in the y-coordinate) to the run (the change in the x-coordinate) between two points on the line. This relationship is expressed with the formula (Y2 - Y1) / (X2 - X1), where (X1, Y1) and (X2, Y2) are the coordinates of two distinct points on the line.

By using this formula, you can determine how much the value of y changes for each unit of change in x. This is essential in various applications in mathematics, physics, and engineering, as the slope provides crucial information about the direction and steepness of the line. A positive slope indicates that as x increases, y also increases, while a negative slope suggests that y decreases as x increases.

The other formulas do not accurately represent the slope because they either do not account for the change in both x and y correctly or focus on unrelated calculations. For instance, one option simply divides the y-coordinates, while another divides the x-coordinates, neither of which reflects the relationship needed to calculate slope. Thus, the correct understanding of slope provided by the chosen formula is vital in plotting, analyzing linear relationships,