Question

Select all tables that represent a proportional relationship between X and Y

Answer 1

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.