Answer: The required value of y is 6.
Step-by-step explanation: We are given that y varies directly as x and y = 9 when \(x=\dfrac{3}{2}.\)
We are to find the value of y when x = 1.
According to the given information, we have
\(y\propto x\\\\\Rightarrow y=k\times x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{where k is the constant of integration}]\\\\\Rightarrow y=kx~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
When y = 9 and \(x=\dfrac{3}{2},\) we have from equation (i) that
\(9=k\times\dfrac{3}{2}\\\\\\\Rightarrow k=\dfrac{18}{3}\\\\\Rightarrow k=6.\)
So, equation (i) becomes
\(y=6x.\)
Therefore, when x = 1, we get
\(y=6\times1=6.\)
Thus, the required value of y is 6.
