To solve this problem, let's break it down step-by-step:
1. Understanding the given information:
- A person hiked for 2 hours.
- The total distance traveled was 5 miles.
2. Calculating the pace:
- The pace is the distance traveled divided by the time taken.
- Given:
- Distance (d) = 5 miles
- Time (t) = 2 hours
- Pace = Distance / Time = 5 miles / 2 hours = 2.5 miles per hour
3. Formulating the equation:
- The relationship between the time hiked (t, in hours) and the distance traveled (d, in miles) can be represented by the equation:
[tex]\[ d = \text{pace} \times t \][/tex]
- Since the pace is 2.5 miles per hour:
[tex]\[ d = 2.5 \times t \][/tex]
4. Determining the type of graph:
- The equation [tex]\( d = 2.5t \)[/tex] represents a continuous relationship because time can take any positive real value. This means the graph of this relationship would be a continuous line, not just distinct points.
5. Conclusion:
- The correct equation that shows the relationship between the time (t) in hours and the distance (d) in miles is [tex]\( d = 2.5t \)[/tex].
- The graph representing this relationship will be continuous.
Therefore, the answer is:
[tex]\[ d = 2.5t, \text{ continuous} \][/tex]
This corresponds to the fourth selection in the given options. So, the final answer is:
[tex]\[ 4 \][/tex]
