Question

Suppose that y varies inversely with x. Write a function that models the inverse function. x = 5 when y = 7

Answer 1

Varying inversely means y=a number divided by x
find the number: 7=k/5 =>k=35
so the equation is y=35/x

Answer 2

Answer:

$y=35\times\frac{1}{x}$

Step-by-step explanation:

Given :  y varies inversely with x

To Find: Write a function that models the inverse function. x = 5 when y = 7

Solution:

We are given that  y varies inversely with x

So, $y \propto \frac{1}{x}$

$\Rightarrow y=k\times\frac{1}{x}$ ---A

where k is the constant of proportionality

Now we are given that x = 5 when y = 7

So,  $\Rightarrow 7=k\times\frac{1}{5}$

$\Rightarrow 35=k$

Substitute the value of k in A

$\Rightarrow y=35\times\frac{1}{x}$

Hence a function that models the inverse function is $y=35\times\frac{1}{x}$ .