Answer:
It is clear that the value of the constant of proportionality k remains the same.
Thus, the value of the constant of proportionality k = 3.5
Explanation:
Given the table
x 6 7 8 9
y 21 24.5 28 31.5
We know that when y varies directly with x, we get the equation
y ∝ x
y = kx
k = y/x
where k is termed as the constant of proportionality.
Now, taking the points from the table to determine the constant of proportionality k:
FOR (6, 21)
substituting x = 6, y = 21 in the equation
k = y/x
k = 21 / 6
k = 7 / 2
k = 3.5
FOR (7, 24.5)
substituting x = 7, y = 24.5 in the equation
k = y/x
k = 24.5/7
k = 3.5
FOR (8, 28)
substituting x = 8, y = 28 in the equation
k = y/x
k = 28/8
k = 7/2
k = 3.5
FOR (9, 31.5)
substituting x = 9, y = 31.5 in the equation
k = y/x
k = 31.5 / 9
k = 3.5
It is clear that the value of the constant of proportionality k remains the same.
Thus, the value of the constant of proportionality k = 3.5