Respuesta :
Answer: The correct option is
(A) [tex]\dfrac{1}{9}.[/tex]
Step-by-step explanation: Given that y is directly proportional to x, and y = 6 when x = 54.
We are to find the constant of proportionality.
According to the given information, we can write that
[tex]y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~~[\textup{where k is the constant of proportionality}]\\\\\Rightarrow k=\dfrac{y}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
When y = 6 and x = 54, then from equation (i), we get
[tex]\dfrac{6}{54}=k\\\\\Rightarrow k=\dfrac{1}{9}.[/tex]
Thus, the required value of the constant of proportionality is [tex]\dfrac{1}{9}.[/tex]
Option (A) is CORRECT.
