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

Jun 30, 2016

$y = - 24$

#### 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:

$y = k x$ (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.

$y = k x$
$- 6 = k \left(3\right)$

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.

$- 6 = k \left(3\right)$
$- 2 = k$

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

$y = - 2 x$
$y = - 2 \left(12\right)$
$y = - 24$

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