Question

What is the constant of variation for the quadratic variation? 6y=9x2
A. 4/9
B. 2/3
C. 3/2
D. -2

Answer 1

@inkyvoyd

Answer 2

The constant of variation is the number that relates two variables in a a proportion.
We can define it as:
\[y=kx\]
Where "k" is the proportionality constante. so in other words, you can bring it to the form y=kx in order to see by naked eye what the constant of proportionality actually is.
We can calculate it by:
\[k=\frac{ y }{ x }\]
But, when we have a quadratic porportionality the story is a little different, though the idea is the same, we will define it as: "when a variable is proportional to the square of the other".
And we write it like this:
\[y=kx^2\]
And we can calculate the constant of proportionality "k" by the same method:
\[k=\frac{ y }{ x^2 }\]

Answer 3

So, if we have:
\[6y=9x^2\]
We want to leave the "y" alone an create a "k" in order to find the constant of proportionality.
so, we divide both sides by "6" ending up with:
\[y=\frac{ 9 }{ 6 }x^2\]
And now, you can easily find it.

Answer 4

I'm still really confused. @Owlcoffee

Answer 5

We ended with:
\[y= \frac{ 9 }{ 6 }x^2\]
So, following the given form:
\[y=kx^2\]
We can easily see that :
\[k=\frac{ 9 }{ 6 }\]
All you have to do, is simplify the fraction.

Answer 6

Oh so it's 3/2?