Final answer:
Distance is directly proportional to time when Luis rides his bike at a constant speed, as shown by a straight-line graph of position versus time.
Step-by-step explanation:
When Luis rides his bike and his position and time are being recorded, we are dealing with a concept in physics that involves the relationship between distance and time. If we assume Luis is riding at a constant speed, the distance he travels is directly proportional to the time. This relationship can be represented by a straight-line graph where the slope of the line indicates speed, depicted as y = mx + b. Here, the y-axis is the distance Luis travels, and the x-axis represents time.
The different options provided in the question suggest potential relationships between distance and time. Based on the provided relative motion and graph information, we can deduce that as Luis rides at a steady speed, the correct option would be A. Distance is directly proportional to time. This means that if the time of Luis's bike ride doubles, the distance he travels also doubles, provided the speed remains constant. This is reflected in the straight-line graph where position increases steadily over time.