Question

The table below represents the distance of an airplane from its destination as a function of time:

Answer 1

Let us first find the equation for the distance as a function of time in the form:

d=mx+b

m=(d2-d1)/(x2-x1)

m=(2160-2700)/(1-0)

m=-540

d=-540x+b, using point (0,2700) we can solve for b

2700=-540(0)+b

2700=b so

d(x)=-540x+2700

A)  The y-intercept is the constant of our distance function  (the distance when x, time, equals zero).  In this case d=2700 is the y-intercept.  This means that the initial distance from the destination was 2700 miles.

B) Since this is just a line and has a constant velocity, its average velocity will just be the constant velocity or slope.  But mathematically we could show this to be true.  Average velocity is change in distance divided by change in time.

v=(540-2160)/(4-1)

v=-1620/3

v=-540 mph

C)

The domain of a function is the possible x values in the proper context.  First time cannot be less than 0.  The other extreme for time is when the plane reaches its destination, when d=0, which is when:

-540x+2700=0

540x=2700

x=5.  

So the plane reaches its destination after 5 hours.  So the domain, the x values, for d=-540x+2700 is

x=[0,5]