After traveling for five hours and 1000 miles, an airplane begins a steady descent. When it begins descending, its altitude is 29,000 feet. After 20 minutes, it is at 9000 feet. The airplane is descending at a rate of Select__ feet per minute. When graphing the descent of the airplane, the starting value would be Select Using the form \( y=m x+b \), the airplane's height can be shown by the function \( y= \)

Let's break down the problem step by step to fill in the blanks accurately. ### 1. Calculating the Descent Rate **Given:** - Initial altitude when descent begins: **29,000 feet** - Altitude after 20 minutes: **9,000 feet** - Time taken for the descent: **20 minutes** **Change in Altitude:** \[ 29,000 \text{ feet} - 9,000 \text{ feet} = 20,000 \text{ feet} \] **Descent Rate:** \[ \frac{20,000 \text{ feet}}{20 \text{ minutes}} = 1,000 \text{ feet per minute} \] **Answer:** The airplane is descending at a rate of **1,000 feet per minute**. ### 2. Determining the Starting Value for the Graph When graphing the descent: - **Starting point** refers to the altitude at the beginning of the descent. **Answer:** The starting value would be **29,000 feet**. ### 3. Formulating the Height Function Using the linear equation form \( y = mx + b \): - **\( m \)**: Slope (descent rate) = **-1,000** (negative because the plane is descending) - **\( b \)**: Starting altitude = **29,000** **Function:** \[ y = -1,000x + 29,000 \] **Answer:** The airplane's height can be shown by the function \( y = -1000\,x + 29000 \). ### Complete Answer - **Descent rate:** 1,000 feet per minute - **Starting value:** 29,000 feet - **Height function:** \( y = -1000\,x + 29000 \)