To solve the problem where [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex], we start by understanding that the relationship can be expressed using the formula [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is a constant of variation.
Given:
- [tex]\( y = 48 \)[/tex] when [tex]\( x = 6 \)[/tex]
First, we find the constant [tex]\( k \)[/tex] by substituting the given values into the formula [tex]\( y = kx \)[/tex].
[tex]\[ 48 = k \cdot 6 \][/tex]
Solving for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{48}{6} \][/tex]
Now we have the value of [tex]\( k \)[/tex]. To find the value of [tex]\( y \)[/tex] when [tex]\( x = 2 \)[/tex], we use the same direct variation formula [tex]\( y = kx \)[/tex]:
[tex]\[ y = \left(\frac{48}{6}\right) \cdot 2 \][/tex]
Simplifying the expression inside the parentheses:
[tex]\[ y = \frac{48}{6} \cdot 2 = 8 \cdot 2 = 16 \][/tex]
So, the correct expression to find the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is [tex]\( 2 \)[/tex] is:
[tex]\[ y = \frac{48}{6} (2) \][/tex]
Therefore, the correct option is:
[tex]\[ y = \frac{48}{6} (2) \][/tex]
