Question

Which table shows a proportional relationship between x and y?
Plz Help

Answer 1

The proportional table in the attached figure

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`k=(y)/(x)` or
`y=kx`

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.

`k=(y)/(x)`

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 ---->
`k=(2)/(1)=2`

For x=2, y=4 ---->
`k=(4)/(2)=2`

For x=3, y=8 ---->
`k=(8)/(3)=2.7`

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 ---->
`k=(1)/(1)=1`

For x=2, y=4 ---->
`k=(4)/(2)=2`

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 ---->
`k=(4)/(1)=4`

For x=2, y=8 ---->
`k=(8)/(2)=4`

For x=3, y=12 ---->
`k=(12)/(3)=4`

The values of k are the same

so

This table represent a proportional relationship between x and y