Respuesta :
Part A: The y-intercept is 665. It is starting at 0 on the x axis. The train starts 665 miles from it's destination, so the intercept is 665.
Part B: As x increases by 1, y decreases by 95. This slope can be shown as -95/1. The rate is 95 miles per hour, since the train covers 95 miles for every hour it travels.
Part C: The train would take 7 hours at the present rate to reach it's destination.
Part B: As x increases by 1, y decreases by 95. This slope can be shown as -95/1. The rate is 95 miles per hour, since the train covers 95 miles for every hour it travels.
Part C: The train would take 7 hours at the present rate to reach it's destination.
Answer:
y-intercept states that the graphs cuts the y-axis.
i.e, (0, y)
As per the statement:
The given table represents the distance of a train from its destination as a function of time;
here, x represents the time in hours and y represents the Distance in miles
Part A.
To find the y-intercept of the function.
by definition:
at x = 0 hours
⇒y = 665 miles
or
y(0) = 665 miles
⇒Y-intercept = 665 miles and It means that the train starts 665 miles from it's destination.
Part B
To find the average rate of change of the function represented by the table between x = 1 to x = 4 hours
Formula for average rate of change(A(x)) of y=f(x) over interval [a, b] is given by:
[tex]A(x)=\frac{f(b)-f(a)}{b-a}[/tex] ....[1]
At x = 1
y =f(1) = 570
At x = 4
then;
y = f(4) = 285
Substitute the given values in [1] we have;
[tex]A(x)=\frac{f(4)-f(1)}{4-1}[/tex]
⇒[tex]A(x)=\frac{285-570}{3}=\frac{-285}{3}[/tex]
⇒[tex]A(x) = -95[/tex]
As x increases by 1, y decreases by 95. This slope = -95
⇒The rate is 95 miles per hour, since the train covers 95 miles for every hour it travel.
Part C.
Using slope intercept form:
Equation of line is given by:
y = mx+b ; where, m is the slope or rate and b is the y-intercept
From above Part A and B:
m = -95 and b = 665
then;
y = -95x+665 ....[2]
We have to find the the domain of the function if the train continued to travel at this rate until it reached its destination
Substitute y = 0 in [2] and solve for x:
0= -95x+665
Add 95x to both sides we have;
95x = 665
Divide both sides by 95 we have;
x = 7 hours
Therefore, the domain of the function if the train continued to travel at this rate until it reached its destination would be 7 hours
