Question

Select all tables that represent a proportional relationship between x and y.

Answer 1

Answer:

Options (1) and (2)

Step-by-step explanation:

Let the proportional relation between x and y is represented by,

y ∝ x

y = kx

Here, k = Proportionality constant

Option 1,

From the given table,

Graph of the points given in the table passes through origin.

For x = 0, y = 0.

For x = 1 and y = 9,

k = $\frac{9}{1}$

k = 9

For x = 2 and y = 18,

k = $\frac{18}{2}$

k = 9

Therefore, table represents a proportional relation.

Option 2.

From the given table,

Graph of the points given in the table passes through origin.

For x = 3 and y = 21,

k = $\frac{21}{3}$

k = 7

For x = 6 and y = 42,

k = $\frac{42}{6}$

k = 7

Therefore, table represents a proportional relation.

Option 3.

From the given table,

For x = 0, y = 1

But for the proportional relation graph should pass through origin (0, 0).

Therefore, table doesn't represent a proportional relation.

Option 4.

From the table given,

For x = 0, y = 2

Graph of the line doesn't pass through the origin (0, 0)

Therefore, table doesn't represent a proportional relation.  

Options (1) and (2) are the correct options.