Question

Help please:Suppose that x and y inversely, and x=10 when y=8 write the function that models the inverse variation

Answer 1

SOLUTION

From the question, we are told that y varies inversely as x

This is mathematically written as

$\begin{gathered} y\propto\frac{1}{x} \\ \propto\text{ is a sign of proportionality } \end{gathered}$

Now, we will remove the proportionality sign and replace it with equal to sign =

If we do this, we will intoduce a constant k

$\begin{gathered} y\propto\frac{1}{x} \\ y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}$

So we have the formula

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

We will substitute the values of x for 10 and y for 8 into the formula to get k, we have

$\begin{gathered} y=\frac{k}{x} \\ 8=\frac{k}{10} \\ k=8\times10 \\ k=80 \end{gathered}$

Now, we will substitute k for 80 back into the formula to get the inverse function, we have

$\begin{gathered} y=\frac{k}{x} \\ y=\frac{80}{x} \end{gathered}$

Hence the answer is option C