Answer:
The 'constant of proportionality k' DOES NOT remain constant for all the points in the table.
Therefore, the table DOES NOT represent a proportional relationship between X and Y.
Explanation:
We know that when y varies directly with x, we get
y ∝ x
y = kx
k = y/x
where k is called the 'constant of proportionality'.
Given the table
x 0 5 10 15
y 2 17 32 47
Let us calculate the k value for all the points
FOR (0, 2)
k = y/x
substitute x = 0, and y = 2
k = 2 / 0 = ∞
FOR (5, 17)
k = y/x
substitute x = 5, and y = 17
k = 17/5
k = 3.4
FOR (10, 32)
k = y/x
substitute x = 10, and y = 32
k = 32/10
k = 16/5
k = 3.2
FOR (15, 47)
k = y/x
substitute x = 15, and y = 47
k = 47/15
k = 3.1
It is clear that the 'constant of proportionality k' DOES NOT remain constant for all the points in the table.
Therefore, the table DOES NOT represent a proportional relationship between X and Y.