Question

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.

Complete the statement that describes the rate of change of the altitude of the airplane with respect to time.





👇
The altitude of the airplane
??
increases
decreases
Time, x (minutes)
Altitude, y (feet)
1.5
28,000
3.25
24,500
6
19,000


👇
at a rate of
??
1,000 feet per minute
2,000 feet per minute
3,000 feet per minute
4,000 feet per minute

Answer 1

To determine the rate of change of altitude with respect to time, we will analyze the given data points in the table:

1. At \(x = 1.5\) minutes, the altitude \(y = 28,000\) feet.
2. At \(x = 3.25\) minutes, the altitude \(y = 24,500\) feet.
3. At \(x = 6\) minutes, the altitude \(y = 19,000\) feet.

Next, we can calculate the change in altitude and the change in time between consecutive points.

From \(1.5\) minutes to \(3.25\) minutes:
- Change in altitude: \(24,500 - 28,000 = -3,500\) feet
- Change in time: \(3.25 - 1.5 = 1.75\) minutes
- Rate of change = \(\frac{-3,500}{1.75} = -2,000\) feet per minute

From \(3.25\) minutes to \(6\) minutes:
- Change in altitude: \(19,000 - 24,500 = -5,500\) feet
- Change in time: \(6 - 3.25 = 2.75\) minutes
- Rate of change = \(\frac{-5,500}{2.75} = -2,000\) feet per minute

Since the rate of change is consistent, we can use this information to complete the statements.

The completed statements are:

The altitude of the airplane **decreases** at a rate of **2,000 feet per minute**.