Find the constant of proportionality for the tables of values

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

Step-by-step 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