Question

Suppose that y varies inversely with x, and y = 5/4 when x = 16.(a) Write an inverse variation equation that relates x and y.Equation: (b) Find y when x = 4.y =

Answer 1

In general, an inverse variation relation has the form shown below

`\begin{gathered} y=(k)/(x) \\ k\to\text{ constant} \end{gathered}`

It is given that x=16, then y=5/4; thus,

`\begin{gathered} (5)/(4)=(k)/(16) \\ \Rightarrow k=(5)/(4)\cdot16 \\ \Rightarrow k=20 \end{gathered}`

Therefore, the equation is y=20/x

`\Rightarrow y=(20)/(x)`

2) Set x=4 in the equation above; then

`\begin{gathered} x=4 \\ \Rightarrow y=(20)/(4)=5 \\ \Rightarrow y=5 \end{gathered}`

When x=4, y=5.