Michael bought a tomato plant and recorded its height on the day of purchase. He is curious about how tall the plant will grow before it starts producing tomatoes, so he monitors its height each day thereafter.

Question

There is a linear relationship between the time, in days, since Michael bought the plant and its height, in centimeters.
Describe the rate of change for this relationship.
The height of the tomato plant
by
per day.

Answer 1

In a linear relationship, the rate of change represents the constant amount by which the dependent variable (in this case, the height of the tomato plant) changes for each unit increase in the independent variable (in this case, time, measured in days).

If we denote the rate of change as \( r \), then you can say:

The height of the tomato plant increases by \( r \) centimeters per day.

The specific value of \( r \) would depend on the actual measurements Michael takes. For example, if the plant grows 2 centimeters each day, you would describe it as:

The height of the tomato plant increases by 2 centimeters per day.

You would fill in \( r \) with the actual growth rate based on Michael's observations.