To determine the distance a sloth travels per minute, we can analyze the points on the graph that you provided.
From the points given:
- At \(0.5\) minutes, the sloth has traveled \(3\) feet.
- At \(1\) minute, the sloth has traveled \(6\) feet.
To find the speed in feet per minute, we can calculate the difference in distance over the difference in time. The speed can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Change in Distance}}{\text{Change in Time}} \]
Using the points \( (0.5, 3) \) and \( (1, 6) \):
- Change in distance = \(6 - 3 = 3\) feet
- Change in time = \(1 - 0.5 = 0.5\) minutes
Now, substitute these values into the formula:
\[ \text{Speed} = \frac{3 \text{ feet}}{0.5 \text{ minutes}} = 6 \text{ feet per minute} \]
Therefore, the distance a sloth travels per minute is \(6\) feet per minute.