Question

In which of the tables below x and y are inversely proportional? Find the constant of variation.

Answer 1

Answer:

In Table (b)

$k=30$

Step-by-step explanation:

 By definition, Inverse proportion equations have he following  form:

$y=\frac{k}{x}$

Where "k" is the Constant of proportionality.

Solving for "k":

$k=yx$

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 $x=3;y=8$:

$(8)(3)=24$

For $x=4;y=6$:

$(6)(4)=24$

For $x=5;y=4.8$:

$(4.8)(5)=24$

For $x=5.5;y=4$:

$(4)(5.5)=22$

Since the product of the values of "x" and "y" is not constant, they are not inversely proportional.

(b) For $x=0.1;y=300$:

$(300)(0.1)=30$

For $x=0.5;y=60$:

$(60)(0.5)=30$

For $x=75;y=0.4$:

$(0.4)(75)=30$

For $x=100;y=0.3$:

$(100)(0.3)=30$

Notice that the Constant of proportionality is:

$k=30$

Therefore "x" and "y" are inversely proportional.