Question

juanita is testing her new model airplane. she starts its descent at an elevation of 2,500 feet. it descends at a constant rate of 500 feet per minute.
time since plane started descent (min) | elevation (ft)
0 | 2,500
1 | 2,000
2 | 1,500
3 | 1,000
4 | 500
what is the slope of this line? in other words, how many feet does the planes elevation decrease per minute?
the slope is .

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x \) is time (minutes) and \( y \) is elevation (feet). Let's take two points from the table: \((0, 2500)\) and \((1, 2000)\).

Step2: Substitute into slope formula

Substitute \( x_1 = 0 \), \( y_1 = 2500 \), \( x_2 = 1 \), \( y_2 = 2000 \) into the formula: \( m=\frac{2000 - 2500}{1 - 0}=\frac{- 500}{1}=-500 \). The negative sign indicates a decrease, and the magnitude is the rate of decrease per minute.

Answer:

-500