Answer:
The table does not show the proportional relationship.
Explanation:
When y varies directly with x, then the equation is
y ∝ x
y = kx
Where 'k' is called the proportionality constant.
Given the table
x 3 6 9 12
y 12 24 45 60
Let us check from the table whether the proportionality constant 'k' remains constant or not.
FOR (3, 12)
y = kx
k = y/x
= 12 / 3 = 4
FOR (6, 24)
k = y/x
= 24 / 6 = 4
FOR (9, 45)
k = y/x
= 45 / 9 = 5
FOR (12, 60)
k = y/x
= 60 / 12 = 5
From the above calculations, it is clear that the value of 'k' does not remain constant.
This means the value of 'k' for the points (6, 24) and (9, 45) is 4, while the value of 'k' for the points (9, 45) and (12, 60) is 5.
Hence, the table does not show the proportional relationship.