The altitude of an airplane is changing at a constant rate. The table shows the linear relationship between

Question

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.

Times (x)
1.5
4.25
3
Altitude, y (feet)
28,000
24,500
19,000

charts to fill

Solve for Y

what number

The altitude of the airplane
increase or decrease

Solve for x

fill this blank with a number

fill this blank with the rate at a rate of
1,000 per miniute
2,000 feet per miniute
3,000 feet per minitue
4,000 feet per minute

pick one of these answers and solve for X and Y

Answer 1

To analyze the changing altitude of the airplane, we first need to find the rate of change of the altitude concerning time using the data from the table you provided.

Given Data:

| Time (x) (minutes) | Altitude (y) (feet) | |---------------------|---------------------| | 1.5 | 28,000 | | 4.25 | 24,500 | | 3 | 19,000 |

Step 1: Calculate the Rate of Change

We can find the change in altitude and time between pairs of points to calculate the rate of change.

1. From (1.5, 28,000) to (3, 19,000):

   • Altitude change: \( y_2 - y_1 = 19,000 - 28,000 = -9,000 \) feet
   • Time change: \( x_2 - x_1 = 3 - 1.5 = 1.5 \) minutes
   • Rate of change: \( \frac{\Delta y}{\Delta x} = \frac{-9,000}{1.5} = -6,000 \) feet per minute

2. From (3, 19,000) to (4.25, 24,500):

   • Altitude change: \( y_2 - y_1 = 24,500 - 19,000 = 5,500 \) feet
   • Time change: \( x_2 - x_1 = 4.25 - 3 = 1.25 \) minutes
   • Rate of change: \( \frac{\Delta y}{\Delta x} = \frac{5,500}{1.25} = 4,400 \) feet per minute

Identifying Consistency

The rates of change calculated above are not consistent, indicating that the data may not represent a linear relationship accurately. Investigating the points shows that the altitude is actually decreasing overall.

Step 2: Choose Representations

Given the options:

• Rate of change is:
  • 1,000 feet per minute
  • 2,000 feet per minute
  • 3,000 feet per minute
  • 4,000 feet per minute

From the calculations, there isn’t an exact fit, but we can choose the closest to identify the altitude of the airplane is decreasing. Although our calculated rate suggests a more complex relationship, we can state that:

The altitude of the airplane is decreasing at a rate of approximately 4,000 feet per minute.

Final Statements

• The altitude of the airplane decreases.
• Fill the blank with a number: 4,000 feet per minute.