a) Looking at the question, for us to determine whether the number of miles driven proportional to the amount of time, we need to check if there are any constant of proportionality which can also be refered to slope.
From the data,
Let M represent miles
t represent the time
We know that:
at t = 1, M = 50
at t = 2, M = 100
at t = 3, M = 150
at t = 4, M = 200
k = M2-M1/t2-t1
k = 100-50/2-1 = 150-100/3-2 = 200-150/4-3
k = 50/1
k = 50
We can say that k = M/t
50 = M/t
M = 50
From the expression derived, it can be seen that the number of miles is directly proportional to the time taken. This shows that the number of miles driven is proportional to the amount of time.
b) the point (2, 100) in the context of the situation means that the total amount of time covered to drive for 100 miles is 2 minutes.
c) the point (5, 250) in the context of the situation means that the total amount of time covered to drive for 250 miles is 5 minutes.
d) the point (1, 50) in the context of the situation means that the total amount of time covered to drive for 50 miles is 1 minutes.