Question

If y varies directly as x, and y = 30 when x = 4, how do you find the constant of proportionality?

Answer 1

It is `7.5`.

Explanation:

if it varies directly means that `y` is equal `x` multiplied by something. I call this "something" `A`.
So I write

`y=Ax`

To find the value of `A` I have to divide on both sides for `x` obtaining

`y/x=Ax/x`

the two `x` on the right cancel each other and I remain with

`y/x=A`.

Now I can substitute the numbers

`30/4=A`
`7.5=A`.

Then the proportionality constant is `7.5`.