Question

Please explain how to find the proportional relationship.

Either Table A or Table B shows a proportional relationship.
Table A
X 1 3 4 5
Y 2 6 8 10

Table B
X 1 2 4 6
Y 3 4 6 8
Plot the points from the table that shows a proportional relationship.​

Answer 1

The table A represent a proportional relationship

The table B not represent a proportional relationship

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

Table A

Find the value of k

For x=1,y=2 ------>
`k=(2)/(1)=2`

For x=3,y=6 ------>
`k=(6)/(3)=2`

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

For x=5,y=10 ------>
`k=(10)/(5)=2`

All the values of k are the same

so

The table A represent a proportional relationship

The equation of the proportional relationship is equal to

`y=2x`

Table B

Find the value of k

For x=1,y=3 ------>
`k=(3)/(1)=3`

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

The values of k are different

so

The table B not represent a proportional relationship