Question

If y varies directly as x, and y=9 when x=4, how do you find y when x=16?

Answer 1

When `x=16`, `y=36`.

Explanation:

If `y` varies directly as `x`, then if `y` increases, `x` increases, and if `y` decreases, `x` decreases. We can express this idea very succinctly in mathematics by writing `y = kx`. Where `k` is a constant. Using this equation and substituting the initial values we have:
`y = kx`
`9 = k*4`
So `k= 9/4`
Hence we can rewrite our general relationship more particularly in this case as `y = 9/4 x`.
Using the second set of values and our specific equation we get:
`y = 9/4 *16`
So `y = 36`