Answer:
see the explanation
The solution's table in 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]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
Let
y ----> the price
x ----> the weight
Find the value of the proportionality constant for each ordered pair in each table
[tex]k=\frac{y}{x}[/tex]
If all the values of k are equal, then the table represents a proportional relationship between the variable x and the variable y
Table 1
For x=1.5 lb, y=$4.50 ----> [tex]k=\frac{4.5}{1.50}=3[/tex]
For x=2 lb, y=$9.00 ----> [tex]k=\frac{9.00}{2}=4.5[/tex]
The values of k are different
therefore
The table not represent a proportional relationship
Table 2
For x=10 g, y=$0.50 ----> [tex]k=\frac{0.50}{10}=0.05[/tex]
For x=15 g, y=$0.55 ----> [tex]k=\frac{0.55}{15}=0.04[/tex]
The values of k are different
therefore
The table not represent a proportional relationship
Table 3
For x=0.5 Kg, y=$0.75 ----> [tex]k=\frac{0.75}{0.5}=1.5[/tex]
For x=5 g, y=$7.50 ----> [tex]k=\frac{7.50}{5}=1.5[/tex]
The values of k are equal
therefore
The table represent a proportional relationship
Table 4
For x=1 oz, y=$2.00 ----> [tex]k=\frac{2}{1}=2[/tex]
For x=2 lb, y=$4.00
Convert lb to oz
Remember that
1 lb=16 oz
so
2 lb=2(16)=32 oz
For x=32 lb, y=$4.00 ----> [tex]k=\frac{4}{32}=0.125[/tex]
The values of k are different
therefore
The table not represent a proportional relationship
