Answer:
Table [tex]1[/tex] and Table [tex]3[/tex]
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]
Let
x-----> the weight
y-----> the price
so
[tex]k=y/x[/tex] ------> the constant of proportionality
Verify each case
Table 1
For [tex]x=10\ mg ,y=\$2.50[/tex] -------> [tex]k=2.50/10=0.25[/tex]
For [tex]x=20\ mg ,y=\$5.00[/tex] -------> [tex]k=5.00/20=0.25[/tex]
The value of k is the same
therefore
The table 1 represent a proportional relationship
Table 2
For [tex]x=2.5\ g ,y=\$5.00[/tex] -------> [tex]k=5.00/2.5=2[/tex]
For [tex]x=5\ g ,y=\$7.50[/tex] -------> [tex]k=7.50/5=1.5[/tex]
The value of k is not the same
therefore
The table 2 not represent a proportional relationship
Table 3
For [tex]x=1\ Kg ,y=\$0.25[/tex] -------> [tex]k=0.25/1=0.25[/tex]
For [tex]x=8\ g ,y=\$2.00[/tex] -------> [tex]k=2.00/8=0.25[/tex]
The value of k is the same
therefore
The table 3 represent a proportional relationship
Table 4
For [tex]x=5\ lb ,y=\$15[/tex] -------> [tex]k=15/5=3[/tex]
For [tex]x=10\ lb ,y=\$20.00[/tex] -------> [tex]k=20/10=2[/tex]
The value of k is not the same
therefore
The table 4 not represent a proportional relationship
