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 [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
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
[tex]k=\frac{B}{A}[/tex]
For A=35, B=92 ---> [tex]k=\frac{92}{35}=2.63[/tex]
For A=23, B=80 ---> [tex]k=\frac{80}{23}=3.48[/tex]
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
[tex]k=\frac{D}{C}[/tex]
For C=20, D=8 ---> [tex]k=\frac{8}{20}=0.40[/tex]
For C=12.5, D=5 ---> [tex]k=\frac{5}{12.5}=0.40[/tex]
the values of k are equal
therefore
There is a proportional relationship between the two quantities
The linear equation is equal to
[tex]D=0.40C[/tex]
