Question

If f(x) varies directly with x, and f(x) = 8 when x = 6, how do you write the direct linear variation equation?

Answer 1

If `f(x)` varies directly with `x`
then
`f(x) = cx` for some constant `c`

We are told that
`f(6) = 8`
so
`8 = c*(6)`

therefore
`c= 8/6 = 4/3`

and the direct linear variation equation is
`f(x) = 4/3 x`