Question

Is 3y=9x a direct variation and if so, what is the constant?

Answer 1

`k=3`

Explanation:

`"a direct variation equation has the form"`

`•color(white)(x)y=kxlarrcolor(blue)"k is the constant of variation"`

`3y=9xlarrcolor(blue)"divide both sides by 3"`

`rArry=3x`

`"this is a direct variation equation with "k=3`

Answer 2

Yes, it is. And constant is 3. See below

Explanation:

`3y=9x` is a direct variation because for two diferente values values of `x`, lets say `x_0` and `x_1` we have

`3y_0=9x_0` and `3y_1=9x_1` substracting both we have

`3y_0-3y_1=9x_0-9x_1`

`3(y_0-y_1)=9(x_0-x_1)` from here we have

`(y_0-y_1)/(x_0-x_1)=9/3=3`