Question

on a flight from chicago, illinois, to denver, colorado, the typical cruising altitude of a passenger jet is approximately 31,000 feet. as the flight departs from ohare international airport, the jet begins to ascend. at 4.3 miles away from the airport, the jet is at an altitude of 4200 feet. the jet reaches an altitude of 36,700 feet at 16.75 miles away from the airport. let the dependent variable represent the altitude of the plane and the independent variable represent the number of miles away from the airport. determine and interpret the slope of the ascent in the context.

Explanation:

Step1: Identify two - point coordinates

Let \((x_1,y_1)=(4.3,4200)\) and \((x_2,y_2)=(16.75,36700)\), where \(x\) is miles from the airport and \(y\) is altitude.

Step2: Apply slope formula

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substitute the values: \(m=\frac{36700 - 4200}{16.75 - 4.3}=\frac{32500}{12.45}\approx 2610.59\).

Step3: Interpret the slope

The slope represents the rate of change of altitude with respect to the distance from the airport. For every additional mile away from the airport during the ascent, the altitude of the jet increases by approximately 2610.59 feet.

Answer:

The slope of the ascent is approximately 2610.59. It means that for every one - mile increase in the distance from the airport during the ascent, the altitude of the jet increases by about 2610.59 feet.