To determine which table represents a proportional relationship between the number of hours Jade bikes and the distance of the bike trip, we need to check whether the ratio of distance to hours remains constant across each row in the table. A relationship is proportional if for every pair (hours, distance), the ratio (distance/hours) is the same.
Let's examine each table to see if they meet this criterion.
### Table A
Number of Hours: 2, 3, 4, 5
Distances (kilometers): 40, 55, 70, 85
Calculate the ratios for each pair:
- [tex]\( \frac{40}{2} = 20 \)[/tex]
- [tex]\( \frac{55}{3} \approx 18.33 \)[/tex]
- [tex]\( \frac{70}{4} = 17.5 \)[/tex]
- [tex]\( \frac{85}{5} = 17 \)[/tex]
The ratios are not the same, so Table A does not represent a proportional relationship.
### Table B
Number of Hours: 2, 3, 4, 5
Distances (kilometers): 40, 60, 120, 150
Calculate the ratios for each pair:
- [tex]\( \frac{40}{2} = 20 \)[/tex]
- [tex]\( \frac{60}{3} = 20 \)[/tex]
- [tex]\( \frac{120}{4} = 30 \)[/tex]
- [tex]\( \frac{150}{5} = 30 \)[/tex]
The ratios change from 20 to 30, so Table B does not represent a proportional relationship.
### Table C
Number of Hours: 2, 3, 4, 5
Distances (kilometers): 40, 80, 120, 160
Calculate the ratios for each pair:
- [tex]\( \frac{40}{2} = 20 \)[/tex]
- [tex]\( \frac{80}{3} \approx 26.67 \)[/tex]
- [tex]\( \frac{120}{4} = 30 \)[/tex]
- [tex]\( \frac{160}{5} = 32 \)[/tex]
The ratios are not the same, so Table C does not represent a proportional relationship.
### Table D
Number of Hours: 2, 3, 4, 5
Distances (kilometers): 40, 60, 80, 100
Calculate the ratios for each pair:
- [tex]\( \frac{40}{2} = 20 \)[/tex]
- [tex]\( \frac{60}{3} = 20 \)[/tex]
- [tex]\( \frac{80}{4} = 20 \)[/tex]
- [tex]\( \frac{100}{5} = 20 \)[/tex]
The ratios are the same (20) for all pairs, so Table D does represent a proportional relationship.
Thus, the table that represents a proportional relationship between the number of hours Jade bikes and the distance of the bike trip is:
Table D.
