Question

The value of `y` varies directly with `x`, and `y = -6` when `x = 3`. What is `y` when `x =12`?

Answer 1

`y = -24`

Explanation:

When anything varies directly with something else, it always indicated multiplication. So in this case, `y` varies directly with `x`. This can be written as:

`y = kx` (all direct variations take this original standard form)

We are also given that `y = - 6` when `x = 3`. What we can do with this information is fairly simple. Just plug in these values into the given formula/equation above.

`y = kx`
`-6 = k(3)`

We are also asked to find `y` when `x` is `12`. We can't solve an equation like this without finding `k`. So let's solve for `k` form the equation we created above first.

`-6 = k(3)`
`-2 = k`

Now that we know `k` is equal to `-2`, we can find what the question is asking.

`y = -2x`
`y = -2(12)`
`y = -24`

For a summary of what we accomplished here:

• We recognized the standard direct variation equation
• We plugged our values in to find `k`
• With `k`, we solved another equation that the question asked us to solve