Which of the following properly describe “slope”? Select all that apply.

Question

StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction
StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction
run / rise
rise / run
ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run)

Answer 1

The following descriptions properly describe "slope":

1. StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction - This is the formula used to calculate the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\).

2. run / rise - This is incorrect. The correct relationship is rise over run, not the other way around.

3. rise / run - This correctly describes how slope is defined, as the change in y (rise) divided by the change in x (run).

4. ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run) - This is a correct description of slope, as it captures the relationship between the rise and run.

In summary, the correct options are:

• StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction
• rise / run
• ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run)