To solve the problem, we need to understand what it means for [tex]\( y \)[/tex] to vary directly as [tex]\( x \)[/tex]. This means that the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] can be expressed in the form [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is a constant of proportionality.
Given that [tex]\( y = 18 \)[/tex] when [tex]\( x = 5 \)[/tex], we can find the constant [tex]\( k \)[/tex]:
1. Determine the constant [tex]\( k \)[/tex]:
[tex]\[
y = kx \implies 18 = k \cdot 5 \implies k = \frac{18}{5}
\][/tex]
2. Use the constant [tex]\( k \)[/tex] to find the new value of [tex]\( y \)[/tex] when [tex]\( x = 11 \)[/tex]:
[tex]\[
y = k \cdot x = \left(\frac{18}{5}\right) \cdot 11
\][/tex]
So, the correct expression that represents this calculation is:
[tex]\[
y = \frac{18}{5} \cdot 11
\][/tex]
Thus, the correct choice from the given options is:
[tex]\[
y = \frac{18}{5}(11)
\][/tex]
