To determine if the linear relationship described in the table is also proportional, we need to check if the ratio of Distance to Time is constant for all given values:
| Time (hours) | 2 | 4 | 6 | 8 |
|--------------|---|---|---|---|
| Distance (miles) | 6 | 12 | 18 | 24 |
First, we calculate the ratio of Distance to Time for each pair:
- For Time = 2 hours and Distance = 6 miles:
[tex]\[
\frac{\text{Distance}}{\text{Time}} = \frac{6 \text{ miles}}{2 \text{ hours}} = 3 \text{ miles/hour}
\][/tex]
- For Time = 4 hours and Distance = 12 miles:
[tex]\[
\frac{\text{Distance}}{\text{Time}} = \frac{12 \text{ miles}}{4 \text{ hours}} = 3 \text{ miles/hour}
\][/tex]
- For Time = 6 hours and Distance = 18 miles:
[tex]\[
\frac{\text{Distance}}{\text{Time}} = \frac{18 \text{ miles}}{6 \text{ hours}} = 3 \text{ miles/hour}
\][/tex]
- For Time = 8 hours and Distance = 24 miles:
[tex]\[
\frac{\text{Distance}}{\text{Time}} = \frac{24 \text{ miles}}{8 \text{ hours}} = 3 \text{ miles/hour}
\][/tex]
As we can see, the ratio of Distance to Time is constant at 3 miles per hour for all pairs of values.
Since the ratio or rate of change is constant, the linear relationship described in the table is indeed proportional.
Therefore, the linear relationship is proportional.
