Answer:
or
(depending on your teacher's format preference)
Step-by-step explanation:
<h3><u>
Proportionality background</u></h3>
Proportionality is sometimes called "variation". (ex. " 'y' varies inversely as 'x' ")
There are two main types of proportionality/variation:
- Direct
- 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 is directly proportional to x
y is directly proportional to x squared
y is directly proportional to x cubed
y is directly proportional to the square root of x
y is inversely proportional to x
y is inversely proportional to x squared
From these examples, we see that two things:
- things that are <u>directly proportional</u> -- the thing is <u>multipli</u>ed to the constant of proportionality "k"
- things that are <u>inversely proportional</u> -- the thing is <u>divide</u>d from the constant of proportionality "k".
<h3><u>
Looking at our question</u></h3>
In our question, y is inversely proportional to x, so the equation we're looking at is the following
.
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:
<h3><u>
Solving for k, and finding the general equation</u></h3>
General Inverse variation equation...
![y=\dfrac {k} {x}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%20%7Bk%7D%20%7Bx%7D)
Substituting known values...
![(12)=\dfrac {k} {(5)}](https://tex.z-dn.net/?f=%2812%29%3D%5Cdfrac%20%7Bk%7D%20%7B%285%29%7D)
Multiplying both sides by 5...
![(12)*5= \left ( \dfrac {k} {5} \right ) *5](https://tex.z-dn.net/?f=%2812%29%2A5%3D%20%5Cleft%20%28%20%5Cdfrac%20%7Bk%7D%20%7B5%7D%20%5Cright%20%29%20%2A5)
Simplifying/arithmetic...
![60=k](https://tex.z-dn.net/?f=60%3Dk)
So, for our situation, k=60. So the inverse proportionality relationship equation for this situation is
.
The way your question is phrased, they may prefer the form: ![xy=60](https://tex.z-dn.net/?f=xy%3D60)