Question

What is the inverse variation equation for the numbers shown in the table?

$x$	$y$
-8	16
-4	32
2	-64
8	-16
16	-8

1. $y=-2x$
2. $y=8$
   
3. $xy=24$
   
4. $xy=-128$
   

Short answer

Option D is the correct answer.

Step-by-step solution

Step 1. Define the meaning of variation.

The changing of variable parameters is called a variation.

Step 2. Define the inverse variation.

The inverse variation of two variables$x$ and$y$ is given by

$xy=k$

Where,$k$ is called the constant of variation.

Step 3. Determine the inverse variation equation for the numbers given in the table.

Observe the table.

At$x=-8,y=16$

Substitute,$x=-8,y=16$ in $xy=k$.

role="math" localid="1648119448347" $$\begin{gathered} \left(-8\right)\left(16\right)=k \\ -128=k \\ k=-128 \end{gathered}$$

Substitute$k=-128$ in $xy=k$.

$xy=-128$

Hence, the inverse variation equation is $xy=-128$.

Therefore option D is the correct answer.