SOLUTION: 4) An airplane at 20,000 feet begins to descend at 22 feet per second. Let x represent the number of seconds and y represent the altitude in feet of the plane. The plane descends

Question 948867: 4) An airplane at 20,000 feet begins to descend at 22 feet per second. Let x represent the number of seconds and y represent the altitude in feet of the plane. The plane descends for 2.5 minutes and then climbs for 5 minutes at 15 feet per second. Which of the following is true concerning the slopes made by the plane's flight?
A The descent at 22 feet per second is steeper than the climb at 15 feet per second because the plane descends at a faster rate than that at which it climbs.
B. The descent at 22 feet per second is less than the climb at 15 feet per second because the slope representing the descent is negative.
C. The climb at 15 feet persecond is steeper than thedescent at 22 feet per second because the climb isrepresented by a positiveslope.
D The 5-minute climb is steeper because 5 minutes is longer than the descent time of 2.5 minutes.

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
x=number of seconds; y=altitude; b=starting altitude(time=x=0, so this is also the y-intercept); m=rate of change (slope)
In mathematics, steepness is defined as the absolute value of the slope (m):

The equation for the altitude at given time x:
y=mx+b
For ascent, m will be positive, for descent m is negative.
For the descent the equation is:
y=-22x+20000 feet so m=-22 and
For the ascent the equation is:
For this we will use b for the altitude because it is not essential to know the exact value; we could use the value 150 sec(time of descent in seconds) for x in the descent equation to find the exact value.
y=15x+b so m=15 and
The "steepness" of the descent is 22 and the "steepness" of the ascent is 15.
Since the greater number is steeper, the descent is more steep than the ascent.
ANSWER: So the correct answer is A because the absolute value of the slope of the line is greater for the descent.

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