The altitude of an airplane is changing at a constant rate. The table shows the linear relationship between `y`, the altitude of the airplane in feet, and `x`, the time in minutes.

Question

Complete the statement that describes the rate of change of the altitude of the airplane with respect to time.
Time, x (minutes):1.5, 3.25, 6
Altitude, y (feet): 28000, 24000,19000
What is the altitude of the plane ?

Answer 1

To find the constant rate of change of the altitude of the airplane with respect to time, we can calculate the difference in altitude divided by the difference in time for the points in the table.

We can use the first two points from the data:

1. When \( x = 1.5 \) minutes, \( y = 28000 \) feet
2. When \( x = 3.25 \) minutes, \( y = 24000 \) feet

The change in altitude \( \Delta y \) is:

\[ \Delta y = y_2 - y_1 = 24000 - 28000 = -4000 \text{ feet} \]

The change in time \( \Delta x \) is:

\[ \Delta x = x_2 - x_1 = 3.25 - 1.5 = 1.75 \text{ minutes} \]

Now, we can find the rate of change:

\[ \text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{-4000 \text{ feet}}{1.75 \text{ minutes}} \approx -2285.71 \text{ feet/minute} \]

This negative value indicates that the altitude of the airplane is decreasing.

You can repeat this process with other pairs of points to verify the constant rate of change. For example, using the second and third points:

1. When \( x = 3.25 \) minutes, \( y = 24000 \) feet
2. When \( x = 6 \) minutes, \( y = 19000 \) feet

The change in altitude and time would give the same rate of change, confirming that the altitude is consistently decreasing at this rate.

To summarize, the rate of change of the altitude of the airplane with respect to time is approximately \(-2285.71\) feet per minute.