3 GUEST, GUEST The value of $$ y $$ varies directly with $$ x $$. When the value of $$ x $$ is 4 , the value of $$ y $$ is -12 . What is the constant of variation when $$ y $$ is a function of $$ x $$, and what is the value of $$ y $$ when $$ x=- $$ Move the correct answer to each box. Each answer may be used more than once. Not all answers $$ \begin{array}{llllll}-18 & -3 & -2 & -\frac{1}{3} & \frac{1}{3}\end{array} $$ $$ \frac{1}{3} \quad 2 $$ 3 18 The constant of variation is $$ \square $$ The value of $$ y $$ when $$ x=-6 $$ is $$ \square $$ .

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Let $$ y $$ vary directly with $$ x $$, which means

$$
y = kx
$$

where $$ k $$ is the constant of variation.

**Step 1: Find the constant of variation $$ k $$.**

We are given that when $$ x = 4 $$, $$ y = -12 $$. Substitute these values into the equation:

$$
-12 = k(4)
$$

Solve for $$ k $$:

$$
k = \frac{-12}{4} = -3
$$

**Step 2: Find $$ y $$ when $$ x = -6 $$.**

Now substitute $$ k = -3 $$ and $$ x = -6 $$ into the equation:

$$
y = -3(-6)
$$

Calculate $$ y $$:

$$
y = 18
$$

Therefore, the constant of variation is $$ -3 $$ and the value of $$ y $$ when $$ x = -6 $$ is $$ 18 $$.
The constant of variation is $$ -3 $$, and the value of $$ y $$ when $$ x = -6 $$ is $$ 18 $$.

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