Respuesta :

Answer:

[tex]y=\dfrac {60} {x}[/tex]   or   [tex]xy=60[/tex]   (depending on your teacher's format preference)

Step-by-step explanation:

Proportionality background

Proportionality is sometimes called "variation".   (ex. " 'y' varies inversely as 'x' ")

There are two main types of proportionality/variation:

  1. Direct
  2. Inverse.

Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").

Below are several different examples of both types of proportionality, and how they might be stated in words:

  • [tex]y=kx[/tex]      y is directly proportional to x
  • [tex]y=kx^2[/tex]     y is directly proportional to x squared
  • [tex]y=kx^3[/tex]     y is directly proportional to x cubed
  • [tex]y=k\sqrt{x}}[/tex]   y is directly proportional to the square root of x
  • [tex]y=\dfrac {k} {x}[/tex]   y is inversely proportional to x
  • [tex]y=\dfrac {k} {x^2}[/tex]   y is inversely proportional to x squared

From these examples, we see that two things:

  • things that are directly proportional -- the thing is multiplied to the constant of proportionality "k"
  • things that are inversely proportional -- the thing is divided from the constant of proportionality "k".

Looking at our question

In our question, y is inversely proportional to x, so the equation we're looking at is the following [tex]y=\dfrac {k} {x}[/tex].

It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it:  "When y=12, x=5."

We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:

Solving for k, and finding the general equation

General Inverse variation equation...

[tex]y=\dfrac {k} {x}[/tex]

Substituting known values...

[tex](12)=\dfrac {k} {(5)}[/tex]

Multiplying both sides by 5...

[tex](12)*5= \left ( \dfrac {k} {5} \right ) *5[/tex]

Simplifying/arithmetic...

[tex]60=k[/tex]

So, for our situation, k=60.  So the inverse proportionality relationship equation for this situation is [tex]y=\dfrac {60} {x}[/tex].

The way your question is phrased, they may prefer the form: [tex]xy=60[/tex]

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