Proportional Relationships Followup Check

Work independently after another learning opportunity. These constructed models and the learner statement are fictional.

For 0 to 5 minutes, a feeder starts with 3 meters of cord already outside and adds 2 meters each minute. Output means total cord outside, including the starting length.

A fictional learner says, “The output gains 2 meters each minute, so total cord is proportional to time.” Evaluate the claim using two positive-time quotients and the zero-input pair. Write a rule for total cord and distinguish its rate of increase from a proportionality constant for the stated output.

For 0 to 4 minutes, a different tank begins empty and gains 2.25 liters each minute. Let x be minutes and y be total liters.

Complete the table, state k with units and write a rule. Plot or describe its four labeled points on the grid. Explain the zero-input point and the one-minute point.

3 Another record without a supplied rule

Another exact record shows only (1 minute, 6 meters), (2 minutes, 12 meters), (5 minutes, 30 meters). Does it establish exactly 36 meters at 6 minutes? Explain the displayed evidence and the condition needed for that prediction.