the table below represents the distance of a car from its destination as a function of time.

time
(hour)
x
distance (miles)
y
0
900
1
850
2
800
3
750

part a: what is the y-intercept of the function and what does this tell you about the car? (4 points)

part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 and what does the average rate represent? (4 points)

part c: what would be the domain of this function if the car traveled the same rate until it reached its destination? (2 points)

First we have to determine a linear equation. We will take two points (0,900) and (1,850):
y=mx+b
900=m*0+b,   b=900
850=m*1+900
m=-50
Linear equation is:
y=-50x+900
Part A: y-interception is y=900 or(0,900).
It means that a car has to travel a distance of 900 miles to reach a final destination.
Part B:Average rate of change:=-50. It represents how many miles per one hour changes the distance from a destination.
Part C: Domain of this function if the car traveled the same rate until it reached its destination:
0=-50x+900
50x=900
x=900/50=18
Domain: x∈ [0, 18].
 

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