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.

Answer 1

Time, x (minutes) 1.5, 3.25, 6
Altitude, y (feet) 28,000, 24,500, 19,000

Answer 2

To provide a complete statement describing the rate of change of the altitude of the airplane with respect to time, we need to identify the slope of the linear relationship from the given data in your table. The slope represents the rate of change of the altitude (y) with respect to time (x).

Assuming you have data points in the form of (x1, y1) and (x2, y2), the rate of change can be calculated as:

\[
\text{Rate of change} = \frac{y2 - y1}{x2 - x1}
\]

Once you calculate this value, you can complete the statement as follows:

"The rate of change of the altitude of the airplane with respect to time is [insert the calculated value] feet per minute."

If you provide specific data points from your table, I can help you calculate the exact rate of change.

Answer 3

To determine the rate of change of the altitude of the airplane with respect to time using the provided data:

**Data points:**
1. (1.5, 28000)
2. (3.25, 24500)
3. (6, 19000)

Let's first calculate the rate of change between the first two points (1.5 minutes, 28,000 feet) and the second two points (3.25 minutes, 24,500 feet):

### From (1.5, 28000) to (3.25, 24500):
- \( x_1 = 1.5 \), \( y_1 = 28000 \)
- \( x_2 = 3.25 \), \( y_2 = 24500 \)

\[
\text{Rate of change} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{24500 - 28000}{3.25 - 1.5}
\]

Calculating the difference:

\[
= \frac{-3500}{1.75} = -2000 \text{ feet per minute}
\]

### From (3.25, 24500) to (6, 19000):
- \( x_1 = 3.25 \), \( y_1 = 24500 \)
- \( x_2 = 6 \), \( y_2 = 19000 \)

\[
\text{Rate of change} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{19000 - 24500}{6 - 3.25}
\]

Calculating the difference:

\[
= \frac{-5500}{2.75} \approx -2000 \text{ feet per minute}
\]

### Summary
The rate of change of altitude is consistent over both intervals:

"The rate of change of the altitude of the airplane with respect to time is **-2000 feet per minute**."

This indicates that the airplane is descending at a constant rate of 2000 feet per minute.