Question

aviation an air traffic controller manages the flow of aircraft in and out of airport airspace by guiding pilots during takeoff and landing. an air traffic controller is monitoring two planes that are in flight near a local airport. the first plane is at an altitude of 1000 meters and is ascending at a rate of 400 meters per minute. the second plane is at an altitude of 5900 meters and is descending at a rate of 300 meters per minute.

a. write a system of equations that represents the altitude of each plane, where x is the amount of time, in minutes, and y is the altitude, in meters. then graph the system on a separate sheet of paper.

y=\boxed{}x+\boxed{}
y=5900-\boxed{}x

Explanation:

Step1: Analyze the first plane's altitude

The first plane starts at 1000 meters (initial altitude) and ascends at 400 meters per minute. The altitude \( y \) as a function of time \( x \) (in minutes) is a linear equation in the form \( y = mx + b \), where \( m \) is the rate (slope) and \( b \) is the initial value (y-intercept). Here, \( m = 400 \) (ascending rate) and \( b = 1000 \) (initial altitude). So the equation is \( y = 400x + 1000 \).

Step2: Analyze the second plane's altitude

The second plane starts at 5900 meters and descends at 300 meters per minute. The rate of descent is the slope, but since it's decreasing, the slope is -300. So the equation is \( y = 5900 - 300x \), which means the coefficient of \( x \) is 300.

Answer:

For the first equation \( y = \boxed{400}x + \boxed{1000} \)
For the second equation \( y = 5900 - \boxed{300}x \)