Question

In an inverse variation, y = 4 when x = 8. Write an inverse variation equation that showsthe relationship between x and y.

Answer 1

The Solution.

Step 1:

We shall write out the general equation that defines the inverse variation between y and x.

`\begin{gathered} y\propto(1)/(x) \\ \\ \Rightarrow y=(1)/(x)* k \\ \\ y=(k)/(x) \end{gathered}`

Step 2:

We shall substitute 4 for y, and 8 for x in the above equation, in order to get the value of k.

`\begin{gathered} 4=(k)/(8) \\ \text{Cross multiplying, we get} \\ k=4*8 \\ k=32 \end{gathered}`

Step 3:

Presentation of the Answer.

The inverse variation between y and x is defined by the equation below:

`y=(32)/(x)`

Therefore, the correct answer is

`y=(32)/(x)`