Answer:
proportional relationship does not exist.
proportional relationship does exist.
proportional relationship does not exist.
proportional relationship does exist.
Explanation:
To establish proportionality :
For data 1:
y α x
y = kx ; k = proportionality constant
Take x = 1 ; y = 5
5 = k
k = 5
Hence, to obtain other data points :
y = 5x (if data is proportional ; if otherwise, the data isn't proportional).
Take ; x = 2
y = 5* 2 = 10
10 ≠ 9
Hence, data isn't proportional.
2.)
Data 2:
y α x
y = kx ; k = proportionality constant
Take x = hours 2 ; y = miles = 110
110 = 2k
k = 110/2
k = 55
Take ; x = 5
y = 55*5 = 275
275 = 275 (proportional relationship exist)
3.)
For the graph:
First graph isn't proportional
4 = 2k ; k = 4/2 = 2 ; k = 2
At x = 6
y = 6*2 = 12
From graph ; y = 8 at x = 6
Hence, proportional relationship does not exist.
4.)
For the 2nd graph:
4 = 2k ; k = 4/2 = 2 ; k = 2
At x = 6
y = 6*2 = 12
From graph ; y = 12 at x = 6
Hence, proportional relationship does exist.