Which expression correctly represents slope?

• A. Rise over Run
• B. Run over Rise
• C. Delta X over Delta Y
• D. X over Y

Answer: (A)

The slope is the vertical change divided by the horizontal change as you move along a line. This is rise over run, since rise corresponds to Δy (vertical change) and run corresponds to Δx (horizontal change). So the slope is Δy/Δx, which is rightly described as rise over run.

If you imagine moving along the line and you go up 3 units for every 2 units to the right, the slope is 3/2, illustrating rise over run. The other phrasing would either swap the numerator and denominator (giving run over rise or Δx/Δy), or just name the coordinates without expressing the change, so they don’t capture how steep the line changes.