f $$ y $$ varies directly with $$ x $$ and $$ y=6 $$ when $$ x=3 $$, find $$ y $$ when $$ x=2 $$. Write and solve a direct variation equation to find the answer. $$ y=\square $$ Submit

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UpStudy AI · Accepted Answer

To solve the direct variation problem, follow these steps:

### 1. **Understand Direct Variation**

When $$ y $$ varies directly with $$ x $$, it means that $$ y $$ is equal to a constant multiplied by $$ x $$. This relationship can be expressed as:

$$
y = kx
$$

Where:
- $$ k $$ is the constant of variation.

### 2. **Find the Constant of Variation ($$ k $$)**

You're given that $$ y = 6 $$ when $$ x = 3 $$. Plug these values into the equation to find $$ k $$:

$$
6 = k \times 3
$$

Solving for $$ k $$:

$$
k = \frac{6}{3} = 2
$$

### 3. **Write the Direct Variation Equation**

Now that you have the value of $$ k $$, substitute it back into the direct variation equation:

$$
y = 2x
$$

$$
\boxed{y = 2x}
$$

### 4. **Find $$ y $$ When $$ x = 2 $$**

Use the direct variation equation to find $$ y $$ when $$ x = 2 $$:

$$
y = 2 \times 2 = 4
$$

$$
\boxed{y = 4}
$$

### **Summary**

- **Direct Variation Equation:** $$ y = 2x $$
- **When $$ x = 2 $$:** $$ y = 4 $$
$$ y = 4 $$

f \( y \) varies directly with \( x \) and \( y=6 \) when \( x=3 \), find \( y \) when \( x=2 \). Write and solve a direct variation equation to find the answer. \( y=\square \) Submit

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