Question

Consider the equality xy k. Write the following inverse proportion: y is inversely proportional to x. When y = 12, x=5.​

Answer 1

`y=\frac {60} {x}` or
`xy=60` (depending on your teacher's format preference)

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:

• 
  `y=kx` y is directly proportional to x
• 
  `y=kx^2` y is directly proportional to x squared
• 
  `y=kx^3` y is directly proportional to x cubed
• 
  `y=k√(x)}` y is directly proportional to the square root of x
• 
  `y=\frac {k} {x}` y is inversely proportional to x
• 
  `y=\frac {k} {x^2}` 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
`y=\frac {k} {x}`.

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...

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

Substituting known values...

`(12)=\frac {k} {(5)}`

Multiplying both sides by 5...

`(12)*5= \left ( \frac {k} {5} \right ) *5`

Simplifying/arithmetic...

`60=k`

So, for our situation, k=60. So the inverse proportionality relationship equation for this situation is
`y=\frac {60} {x}`.

The way your question is phrased, they may prefer the form:
`xy=60`