Question

Suppose that y is directly proportional to x, and y = 6 when x = 54. What is the constant of proportionality?

A) 1/9
B) 1/6
C) 6
D) 9

Answer 1

C

Explanation:

Answer 2

Answer: The correct option is

(A)
`(1)/(9).`

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

`y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~~[\textup{where k is the constant of proportionality}]\\\\\Rightarrow k=(y)/(x)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

When y = 6 and x = 54, then from equation (i), we get

`(6)/(54)=k\\\\\Rightarrow k=(1)/(9).`

Thus, the required value of the constant of proportionality is
`(1)/(9).`

Option (A) is CORRECT.