Which of the following are ways to find the rate of change?

change in y over change in x
rise over run
subtract y coordinates over subtract x coordinates
all of the above

1 answer

All of the options listed are ways to find the rate of change. They all describe the same concept mathematically:

  1. Change in y over change in x: This is the most general definition of the rate of change, often represented mathematically as \(\frac{\Delta y}{\Delta x}\).

  2. Rise over run: This phrase is commonly used in the context of a graph, where "rise" refers to the change in the y-coordinate and "run" refers to the change in the x-coordinate.

  3. Subtract y coordinates over subtract x coordinates: This is essentially a more explicit way of expressing the same concept, where you calculate \(\frac{y_2 - y_1}{x_2 - x_1}\).

Since all these descriptions convey the same idea of the rate of change (slope of a line), the correct answer is all of the above.