Which statements are correct interpretations of this graph?

Question

Select each correct answer.

Responses

3 boxes are filled every 4 min.
3 boxes are filled every 4 min.

4 boxes are filled every 3 min.
4 boxes are filled every 3 min.

0.75 boxes are filled per minute.
0.75 boxes are filled per minute.

1.3 boxes are filled per minute.
1.3 boxes are filled per minute.
A first-quadrant graph with horizontal axis labeled Time in minutes and vertical axis labeled Boxes filled. Aray beginning at the origin through points at begin ordered pair 4 comma 3, begin ordered pair 12 comma 9, and begin ordered pair 16 comma 12 end ordered pair

Answer 1

To analyze the graph based on the provided information, we need to determine the rate at which boxes are filled per minute.

1. The ordered pairs you've provided indicate that:
   • At 4 minutes, 3 boxes are filled.
   • At 12 minutes, 9 boxes are filled.
   • At 16 minutes, 12 boxes are filled.

Now, let's calculate the rates:

• From 0 to 4 minutes: 3 boxes/4 minutes = 0.75 boxes per minute.
• From 4 to 12 minutes (8 minutes interval): (9 boxes - 3 boxes)/(12 minutes - 4 minutes) = 6 boxes/8 minutes = 0.75 boxes per minute.
• From 12 to 16 minutes (4 minutes interval): (12 boxes - 9 boxes)/(16 minutes - 12 minutes) = 3 boxes/4 minutes = 0.75 boxes per minute.

Based on this analysis:

• 3 boxes are filled every 4 min. (Correct)
• 4 boxes are filled every 3 min. (This is not correct, as the calculated rate does not support this)
• 0.75 boxes are filled per minute. (Correct)
• 1.3 boxes are filled per minute. (This is not correct, as the calculated rate does not support this)

Thus, the correct interpretations of the graph are:

• 3 boxes are filled every 4 min.
• 0.75 boxes are filled per minute.