Answer:
In Table (b)
[tex]k=30[/tex]
Step-by-step explanation:
By definition, Inverse proportion equations have he following form:
[tex]y=\frac{k}{x}[/tex]
Where "k" is the Constant of proportionality.
Solving for "k":
[tex]k=yx[/tex]
Having the values of "x" and "y" given in each table, you can check if the products of "x" and "y" is equal to a constant value.
Then:
(a) For [tex]x=3;y=8[/tex]:
[tex](8)(3)=24[/tex]
For [tex]x=4;y=6[/tex]:
[tex](6)(4)=24[/tex]
For [tex]x=5;y=4.8[/tex]:
[tex](4.8)(5)=24[/tex]
For [tex]x=5.5;y=4[/tex]:
[tex](4)(5.5)=22[/tex]
Since the product of the values of "x" and "y" is not constant, they are not inversely proportional.
(b) For [tex]x=0.1;y=300[/tex]:
[tex](300)(0.1)=30[/tex]
For [tex]x=0.5;y=60[/tex]:
[tex](60)(0.5)=30[/tex]
For [tex]x=75;y=0.4[/tex]:
[tex](0.4)(75)=30[/tex]
For [tex]x=100;y=0.3[/tex]:
[tex](100)(0.3)=30[/tex]
Notice that the Constant of proportionality is:
[tex]k=30[/tex]
Therefore "x" and "y" are inversely proportional.
