Question

If y varies directly with x, and if y = 2/3 when x = 1/4, how do you find the direct variation equation?

Answer 1

`3y=8x`

Explanation:

If `y` varies directly with `x` then
`color(white)("XXX")y=c*x` for some constant of variation `c`

If `(x,y)=(1/4,2/3)` is a solution to this equation, then
`color(white)("XXX")2/3 = c*1/4`

`color(white)("XXX")rarr c=2/3 *4/1 = 8/3`

So
`color(white)("XXX")y=8/3x`
or (clearing the fraction)
`color(white)("XXX")3y=8x`