Answer:
we conclude that the relationship between distance and time is NOT proportional.
Hence, she did not drive at a constant speed.
Explanation:
We know that when 'y' varies directly with 'x', we get the equation
y ∝ x
y = kx
k = y/x
where 'k' is called the constant of proportionality.
In our case, the table shows the distance Allison drove on one day of her vacation.
Time (h) 1 2 3 4 5
Distance (mi) 55 100 165 280 250
using the equation
k = y/x
susbtitute y = 55, x = 1
k = 55/1 = 55
substitute y = 100, x = 2
k = y/x
k = 100 / 2 = 50
substitute y = 165, x = 3
k = y/x
k = 165 / 3 = 55
substitute y = 280, x = 4
k = y/x
k = 280 / 4 = 70
substitute y = 250, x = 5
k = y/x
k = 250 / 5 = 50
It is clear that the value of 'k' does not remain constant.
Therefore, we conclude that the relationship between distance and time is NOT proportional.
Hence, she did not drive at a constant speed.