Answer:
The proportional table in the attached figure
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Verify each table
Find the value of the constant of proportionality k for each ordered pair of a table.
[tex]k=\frac{y}{x}[/tex]
If all the values of k are the same, then the table represent a proportional relationship between x and y
Table 1
For x=1, y=2 ----> [tex]k=\frac{2}{1}=2[/tex]
For x=2, y=4 ----> [tex]k=\frac{4}{2}=2[/tex]
For x=3, y=8 ----> [tex]k=\frac{8}{3}=2.7[/tex]
The values of k are not equal
so
This table not represent a proportional relationship between x and y
Table 2
For x=0, y=4
The line not passes through the origin
so
This table not represent a proportional relationship between x and y
Table 3
For x=0, y=0 ----> is OK the line passes though the origin
For x=1, y=1 ----> [tex]k=\frac{1}{1}=1[/tex]
For x=2, y=4 ----> [tex]k=\frac{4}{2}=2[/tex]
The values of k are not equal
so
This table not represent a proportional relationship between x and y
Table 4
For x=1, y=4 ----> [tex]k=\frac{4}{1}=4[/tex]
For x=2, y=8 ----> [tex]k=\frac{8}{2}=4[/tex]
For x=3, y=12 ----> [tex]k=\frac{12}{3}=4[/tex]
The values of k are the same
so
This table represent a proportional relationship between x and y
