Question

A graph with an x-axis representing time in minutes ranges from 0 to 4.5 in increments of 0.5. The y-axis representing distance in feet ranges from 0 to 9 in unit increments. A line is labeled speed of a sloth. The line passes through the following points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 0.5 comma 3 right parenthesis; left parenthesis 1 comma 6 right parenthesis; and left parenthesis 1.5 comma 9 right parenthesis.
Identify the distance a sloth travels per minute.

(1 point)

Answer 1

To determine the speed of the sloth, we need to calculate the distance traveled per minute based on the points given in the graph.

We observe the points:
- At \( t = 0 \) minutes, distance \( = 0 \) feet.
- At \( t = 0.5 \) minutes, distance \( = 3 \) feet.
- At \( t = 1 \) minute, distance \( = 6 \) feet.
- At \( t = 1.5 \) minutes, distance \( = 9 \) feet.

Now, we will calculate the distance traveled during each interval and the speed in feet per minute.

1. From \( t = 0 \) to \( t = 0.5 \):
\[
\text{Distance} = 3 - 0 = 3 \text{ feet}
\]
\[
\text{Time} = 0.5 - 0 = 0.5 \text{ minutes}
\]
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{3 \text{ feet}}{0.5 \text{ minutes}} = 6 \text{ feet per minute}
\]

2. From \( t = 0.5 \) to \( t = 1 \):
\[
\text{Distance} = 6 - 3 = 3 \text{ feet}
\]
\[
\text{Time} = 1 - 0.5 = 0.5 \text{ minutes}
\]
\[
\text{Speed} = \frac{3 \text{ feet}}{0.5 \text{ minutes}} = 6 \text{ feet per minute}
\]

3. From \( t = 1 \) to \( t = 1.5 \):
\[
\text{Distance} = 9 - 6 = 3 \text{ feet}
\]
\[
\text{Time} = 1.5 - 1 = 0.5 \text{ minutes}
\]
\[
\text{Speed} = \frac{3 \text{ feet}}{0.5 \text{ minutes}} = 6 \text{ feet per minute}
\]

In all intervals, the sloth travels 6 feet per minute. Therefore, the distance a sloth travels per minute is:

**6 feet per minute.**