To solve this problem, we need to understand the concept of direct variation. In a direct variation, the relationship between two variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex] can be written as:
[tex]\[ y = kx \][/tex]
where [tex]\(k\)[/tex] is the constant of variation.
### Step-by-Step Solution
1. Identify the given values:
- When [tex]\( x = 72 \)[/tex], [tex]\( y = 6 \)[/tex].
2. Find the constant of variation [tex]\( k \)[/tex]:
Substitute the known values into the direct variation formula:
[tex]\[ 6 = k \cdot 72 \][/tex]
To isolate [tex]\( k \)[/tex], divide both sides by 72:
[tex]\[ k = \frac{6}{72} \][/tex]
Simplify the fraction:
[tex]\[ k = \frac{1}{12} \][/tex]
3. Use the constant [tex]\( k \)[/tex] to find [tex]\( y \)[/tex] when [tex]\( x = 8 \)[/tex]:
Substitute [tex]\( k = \frac{1}{12} \)[/tex] and [tex]\( x = 8 \)[/tex] back into the direct variation formula:
[tex]\[ y = \frac{1}{12} \cdot 8 \][/tex]
Simplify the multiplication:
[tex]\[ y = \frac{8}{12} \][/tex]
Further simplify the fraction:
[tex]\[ y = \frac{2}{3} \][/tex]
Therefore, the value of [tex]\( y \)[/tex] when [tex]\( x = 8 \)[/tex] is [tex]\( \frac{2}{3} \)[/tex].
The correct answer is [tex]\( \boxed{\frac{2}{3}} \)[/tex].
