Question

PLEASE HELP

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)

Answer 1

Explanation:

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

Answer 2

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:
`(y2-y1)/(x2-x1) = (750-850)/(3-1)= (-100)/(2)`=-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].