Question

Determine if there is a proportional relationship between the two quantities

Answer 1

The table a not represent a proportional relationship between the two quantities

The table b represent a proportional relationship between the two quantities

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`

Verify each table

Table a

Let

A ----> the independent variable or input value

B ----> the dependent variable or output value

the value of k will be

`k=(B)/(A)`

For A=35, B=92 --->
`k=(92)/(35)=2.63`

For A=23, B=80 --->
`k=(80)/(23)=3.48`

the values of k are different

therefore

There is no proportional relationship between the two quantities

Table b

Let

C ----> the independent variable or input value

D ----> the dependent variable or output value

the value of k will be

`k=(D)/(C)`

For C=20, D=8 --->
`k=(8)/(20)=0.40`

For C=12.5, D=5 --->
`k=(5)/(12.5)=0.40`

the values of k are equal

therefore

There is a proportional relationship between the two quantities

The linear equation is equal to

`D=0.40C`