Question

Direct variation. If y=6 when x=2/3, find x when y=12. ?

Answer 1

`x = 4/3 = 1 1/3`

Explanation:

In a direct variation if y is double then x is doubled.

`2 xx y = 2 xx 6 = 12`

so

`2 xx x = 2 xx 2/3 = 4/3 = 1 1/3`

Answer 2

`x=4/3`

Explanation:

It is assumed that since the y is doubled, then x is doubled, so x would be `4/3`.

Answer 3

`x=4/3`

Explanation:

`"the initial statement is "ypropx`

`"to convert to an equation multiply by k the constant"`
`"of variation"`

`rArry=kx`

`"to find k use the given condition"`

`y=6" when "x=2/3`

`y=kxrArrk=y/x=6/(2/3)=(3xx6)/2=9`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=9x)color(white)(2/2)|)))`

`"when "y=12" then"`

`9x=12rArrx=12/9=4/3`