Why is one relationship directly proportional while another is inversely proportional?
Keep speed constant and change time: distance is directly proportional. Keep distance fixed and change speed: travel time is inversely proportional. Compare the two modes.
Direct proportion: When speed is constant, doubling or tripling the time also doubles or triples the distance. Distance = speed × time, or y = ax.
Inverse proportion: When the distance is fixed, doubling the speed cuts the travel time in half. Time = distance ÷ speed, or y = k/x.