Question

How do you write an equation of the direct variation that includes the given point (5, 1)?

Answer 1

`y=x/5`

Explanation:

Direct variation is of form `y=kx` where `k` is some constant.

So it is an equation of a strait line.

We may determine the value of `k` as we are given values for `y and x`

So by substitution we have:

`(x,y)->y=kx->y=kxx x`
`(x,y)->color(white)(.)(5,1)color(white)(.)->1=kxx5`

Divide both sides by `color(red)(5)` and we have:

`color(green)(1/(color(red)(5))=kxx 5/(color(red)(5)))`

But `5/5=1 and kxx1=k`

`1/5=k`

So `y=kx" "->" "y=1/5x" "->" "y=x/5`