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 altitude of the airplane with respect to time, we will first use the data provided.

We have the following points:

• At \( x = 1.5 \) minutes, \( y = 28,000 \) feet
• At \( x = 3 \) minutes, \( y = 19,000 \) feet
• At \( x = 4.25 \) minutes, \( y = 24,500 \) feet

Step 1: Determine the rate of change (slope)

First, we will calculate the change in altitude over the change in time between two of the data points. Let's pick the points at \( x = 1.5 \) (28,000 feet) and \( x = 3 \) (19,000 feet).

The formula to calculate the slope (rate of change) is:

\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]

Using points \((1.5, 28000)\) and \((3, 19000)\):

\[ \Delta y = 19000 - 28000 = -9000 \] \[ \Delta x = 3 - 1.5 = 1.5 \] \[ \text{slope} = \frac{-9000}{1.5} = -6000 \text{ feet per minute} \]

Step 2: Evaluate the altitude change

The slope \( -6000 \) indicates that the altitude of the airplane is decreasing by 6,000 feet for each minute.

Step 3: Fill in the statement

• The altitude of the airplane decreases.
• The rate of change is approximately 6,000 feet per minute.

Since none of the provided choices (1,000; 2,000; 3,000; or 4,000 feet per minute) match our calculated rate, we can note that based on the analysis, the changes we observed do not fit into the options given.

Conclusion

For the blanks:

• The altitude of the airplane is decreasing.
• The rate is approximately 6,000 feet per minute.

If we need to pick from the listed numbers, we might need to round or approximate to 4,000 feet per minute, but be aware that this value does not represent the actual calculation.

If you need a specific number for \( y \) based on \( x = 4.25 \) minutes or any other specific number, you can use the linear equation derived from the slope:

Using the point-slope form \( y - y_1 = m(x - x_1) \):

Using the point \( (3, 19000) \): \[ y - 19000 = -6000(x - 3) \]

To find \( y \) when \( x = 4.25 \): \[ y - 19000 = -6000(4.25 - 3) \] \[ y - 19000 = -6000(1.25) \] \[ y - 19000 = -7500 \] \[ y = 11500 \text{ feet} \]

So, at \( x = 4.25 \), the altitude \( y \) is 11,500 feet.