Respuesta :

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:

[tex]y=35\times\frac{1}{x}[/tex]

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, [tex]y \propto \frac{1}{x}[/tex]

[tex]\Rightarrow y=k\times\frac{1}{x}[/tex] ---A

where k is the constant of proportionality

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

So,  [tex]\Rightarrow 7=k\times\frac{1}{5}[/tex]

[tex]\Rightarrow 35=k[/tex]

Substitute the value of k in A

[tex]\Rightarrow y=35\times\frac{1}{x}[/tex]

Hence a function that models the inverse function is [tex]y=35\times\frac{1}{x}[/tex] .