Question

Determine if there is a proportional relationship between the two quantities

Answer 1

Answer:

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

The table b represent a proportional relationship between the two quantities

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 $k=\frac{y}{x}$ 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

$k=\frac{B}{A}$

For A=35, B=92 ---> $k=\frac{92}{35}=2.63$

For A=23, B=80 ---> $k=\frac{80}{23}=3.48$

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

$k=\frac{D}{C}$

For C=20, D=8 ---> $k=\frac{8}{20}=0.40$

For C=12.5, D=5 ---> $k=\frac{5}{12.5}=0.40$

the values of k are equal

therefore

There is a proportional relationship between the two quantities

The linear equation is equal to

$D=0.40C$