Mickey is traveling at a constant speed on his bicycle. The graph shows how d, the total distance traveled, depends on t, the time in hours.

Question

The graph titled Bike Trip reading shows distance traveled in miles on the vertical axis labeled d and time in hours on the horizontal axis labeled t. A line passing through (0, 0) and (1, 12), is shown.

What can be concluded from the information on the graph?

A.
Mickey is riding at a speed of 11 miles per hour.

B.
Mickey rode a total of 12 miles.

C.
Mickey rode a total of 11 miles.

D.
Mickey is riding at a speed of 12 miles per hour.

Answer 1

To determine what can be concluded from the graph, we need to analyze the information given.

The graph shows a line that passes through the points (0, 0) and (1, 12). This means that at time \( t = 0 \) hours, the distance \( d = 0 \) miles (the starting point), and at time \( t = 1 \) hour, the distance \( d = 12 \) miles.

The slope of the line (which represents speed) can be calculated as follows:

\[ \text{Speed} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{12 \text{ miles} - 0 \text{ miles}}{1 \text{ hour} - 0 \text{ hours}} = \frac{12 \text{ miles}}{1 \text{ hour}} = 12 \text{ miles per hour} \]

Now let's evaluate the answer choices:

A. Mickey is riding at a speed of 11 miles per hour. (Incorrect)

B. Mickey rode a total of 12 miles. (Correct if interpreted as distance traveled at \( t = 1 \) hour)

C. Mickey rode a total of 11 miles. (Incorrect)

D. Mickey is riding at a speed of 12 miles per hour. (Correct)

From this analysis, the correct interpretations are:

1. Mickey is riding at a speed of 12 miles per hour (D).
2. At \( t = 1 \) hour, Mickey has traveled a total distance of 12 miles (B).

Based on the primary conclusion regarding speed, the best answer is:

D. Mickey is riding at a speed of 12 miles per hour.