Answer:
Option (4)
Step-by-step explanation:
Proportional relationship means,
y ∝ x
y = kx
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
Here, k = proportionality constant
Therefore, if the graph of a line passes through the origin (0, 0) table will represent the proportional relationship.
From table 1,
For a point (1, 2)
![k=\frac{2}{1}=2](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B2%7D%7B1%7D%3D2)
For another point (3, 2)
![k=\frac{3}{2}=1.5](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B3%7D%7B2%7D%3D1.5)
In both the cases 'k' is not same of constant.
Therefore, table (1) is not proportional.
For table (2),
Line passes through (2, 0).
That means there is a x-intercept → (2, 0)
Therefore, table doesn't represent a proportional relationship.
For table (3),
Line passes through a point (0, 1)
It means given line has a y-intercept → y = 1
Therefore, table doesn't represent a proportional relationship.
For table (4),
Line of this table passes through two points (1, 3) and (2, 6)
![k=\frac{3}{1}=3](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B3%7D%7B1%7D%3D3)
![k=\frac{6}{2}=3](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B6%7D%7B2%7D%3D3)
Therefore, proportionality constant for the given table is 3.
Now we can graph table (4).