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 = [tex]\frac{9}{1}[/tex]
k = 9
For x = 2 and y = 18,
k = [tex]\frac{18}{2}[/tex]
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 = [tex]\frac{21}{3}[/tex]
k = 7
For x = 6 and y = 42,
k = [tex]\frac{42}{6}[/tex]
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.
