https://file.aiquickdraw.com/mathbot/file/1730469930184op48le9f.jpg

To solve this problem, we need to follow these steps:

### Step 1: Set Up the Proportion
Since \( y \) varies directly as \( x \), we can write this relationship as:
\[
y = kx
\]
where \( k \) is the constant of variation.

### Step 2: Find the Constant of Variation (\( k \))
We are given that when \( x = -6 \), \( y = 5 \). Substitute these values into the equation to solve for \( k \):
\[
5 = k \cdot (-6)
\]
\[
k = \frac{5}{-6} = -\frac{5}{6}
\]

### Step 3: Substitute \( k \) and Solve for \( y \) when \( x = 6 \)
Now that we know \( k = -\frac{5}{6} \), we can use this value to find \( y \) when \( x = 6 \):
\[
y = -\frac{5}{6} \cdot 6
\]
\[
y = -5
\]

### Final Answer:
\[
y = -5
\]

Would you like a further breakdown of any of these steps?

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Here are some related questions to explore further:

1. What does it mean for \( y \) to vary directly with \( x \)?
2. How do you interpret the constant of variation in direct variation problems?
3. Can you use this process to solve for \( x \) if a value of \( y \) is given instead?
4. How does direct variation differ from inverse variation?
5. What would happen to \( y \) if \( x \) was doubled?

**Tip:** Direct variation implies that as one variable increases, the other also changes in a predictable, proportional manner.

y varies directly as x. If x = -6 then y = 5. Find y when x = 6.

Solve a direct variation problem where y varies directly as x. Given that x = -6 results in y = 5, find the value of y when x = 6. This problem covers the concept of direct variation and proportional relationships, suitable for students in Grades 7-9.

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