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

User Kawa
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5 votes

Answer:


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

User PooSH
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