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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)

Verified Answer :

HomertheGenius

First we have to determine a linear equation. We will take two points (0,900) and (1,850):
y=mx+b
900=m0+b,   b=900
850=m1+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:\(\frac{y2-y1}{x2-x1} = \frac{750-850}{3-1}= \frac{-100}{2}\)=-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].

Answer:

Step-by-step explanation:

First we have to determine a linear equation. We will take two points (0,900) and (1,850):

y=mx+b

900=m0+b, b=900

850=m1+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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