Answer:
second table (see the attached figure)
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]y/x=k[/tex] or [tex]y=kx[/tex]
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
First table
Let
x ----> the weight in lb
y ----> the price in dollars
For x=1.5, y=3.50
Find the value of the constant of proportionality k
[tex]k=y/x[/tex] ----> [tex]k=3.5\1.5=2.33[/tex]
For x=2, y=7
[tex]k=y/x[/tex] ----> [tex]k=7/2=3.5[/tex]
The values of k are different
therefore
This table not represent a proportional relationship between weight and price
Second table
Let
x ----> the weight in g
y ----> the price in dollars
For x=1.5, y=0.90
Find the value of the constant of proportionality k
[tex]k=y/x[/tex] ----> [tex]k=0.90\1.5=0.6[/tex]
For x=8, y=4.80
[tex]k=y/x[/tex] ----> [tex]k=4.8/8=0.6[/tex]
The values of k are equal
therefore
This table represent a proportional relationship between weight and price
Third table
Let
x ----> the weight in kg
y ----> the price in dollars
For x=2, y=0.75
Find the value of the constant of proportionality k
[tex]k=y/x[/tex] ----> [tex]k=0.75/2=0.375[/tex]
For x=5, y=3.75
[tex]k=y/x[/tex] ----> [tex]k=3.75/5=0,75[/tex]
The values of k are different
therefore
This table not represent a proportional relationship between weight and price
Fourth table
Let
x ----> the weight in oz
y ----> the price in dollars
For x=2 oz, y=4
Find the value of the constant of proportionality k
[tex]k=y/x[/tex] ----> [tex]k=4/2=2[/tex]
For x=4 lb, y=8
convert to oz
1 lb=16 oz
4 lb=64 oz
[tex]k=y/x[/tex] ----> [tex]k=8/64=0,125[/tex]
The values of k are different
therefore
This table not represent a proportional relationship between weight and price
