To determine if the quantities in the data table represent a proportional relationship, we need to check if the ratio of miles traveled per hour is constant for all the given data points.
Let's calculate the ratio (miles per hour) for each entry in the table:
-
For 1 hour biked:
\[ \frac{12 , \text{miles}}{1 , \text{hour}} = 12 , \text{miles per hour} \] -
For 2 hours biked:
\[ \frac{26 , \text{miles}}{2 , \text{hours}} = 13 , \text{miles per hour} \] -
For 3 hours biked:
\[ \frac{30 , \text{miles}}{3 , \text{hours}} = 10 , \text{miles per hour} \] -
For 4 hours biked:
\[ \frac{48 , \text{miles}}{4 , \text{hours}} = 12 , \text{miles per hour} \]
Now we compare the ratios:
- For 1 hour: 12 mph
- For 2 hours: 13 mph
- For 3 hours: 10 mph
- For 4 hours: 12 mph
Since the ratios are not constant (12, 13, 10, 12), the data does not represent a proportional relationship.
Therefore, the correct response is:
No, not all of the ratios are proportional or have equivalence.