SOLUTION: 1.) A rocket is 1 mile above the earth 30 seconds after lifting off. The rocket is 5 miles above the earth after 2.5 minutes. a) Write an equation that represents this situatio

Question 828174: 1.) A rocket is 1 mile above the earth 30 seconds after lifting off. The rocket is 5 miles above the earth after 2.5 minutes.
a) Write an equation that represents this situation.
b) What does the slope represent in this situation? The y-intercept?
P.S. Could you also show me how you got the answers? Thanks!
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
At liftoff the rocket is at ground level, 0 miles above earth's surface.
After 30 seconds, it is 1 mile above earth's surface.

a) The average upwards speed of the rocket during the first 30 seconds (0.5 minutes) is
miles per minute.
The average upwards speed of the rocket during the next 2 minutes (between 30 seconds and 2.5 minutes after liftoff) in miles per minute is
.
It may not be scientifically sound to assume that the speed was 2 miles per minute at all times, but my guess is that your teacher intended exactly that.
So the height of the rocket (in miles), as a function of time (in minutes) since liftoff is

If you called the height in miles and the time in minutes ,
then the equation would be .
Either way, the function is a linear function.
Its graph is a straight line through the origin.
I would graph it only for because we do not know where that rocket was before liftoff (for ).

b) The slope in is miles per minute and represents the speed of the rocket.
The y-intercept is 0 miles, because the graph crosses the y-axis at .
The y-intercept represents the height of the rocket at liftoff: 0 miles above earth.
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