Question

while on a trip, you notice that the video screen on the airplane, in addition to showing movies and news, records your altitude (in kilometers) above the ground. as the plane starts its descent (at time x = 0), you record the following data:

time, x (min.)	altitude, y (km)
0	12
2	10
4	8
6	6
8	4
10	2

if you were to graph these points on a graph, you would notice that the line that forms represents a linear function. what is the practical meaning of slope in this situation?
a. for every minute that passes, the airplane descends 1 kilometer.
b. for every minute that passes, the airplane ascends 1 kilometer.
c. for every 2 minutes that passes, the airplane descends 1 kilometer.
d. for every minute that passes, the airplane ascends 2 kilometers.

Explanation:

1. First, recall the formula for the slope of a linear function, \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
2. Take two points from the table, e.g., \((x_1,y_1)=(0,12)\) and \((x_2,y_2)=(2,10)\).
3. Calculate the slope: \(m=\frac{10 - 12}{2 - 0}=\frac{-2}{2}=-1\) per 2 minutes (or \(-0.5\) per minute). The negative sign indicates descent. So for every 2 minutes, the altitude decreases by 1 km (descends 1 km), which matches option c.

Answer:

c. For every 2 minutes that passes, the airplane descends 1 kilometer.