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}.](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B3%7D%7B2%7D.)
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)](https://tex.z-dn.net/?f=y%5Cpropto%20x%5C%5C%5C%5C%5CRightarrow%20y%3Dk%5Ctimes%20x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%5B%5Ctextup%7Bwhere%20k%20is%20the%20constant%20of%20integration%7D%5D%5C%5C%5C%5C%5CRightarrow%20y%3Dkx~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28i%29)
When y = 9 and
we have from equation (i) that
![9=k\times\dfrac{3}{2}\\\\\\\Rightarrow k=\dfrac{18}{3}\\\\\Rightarrow k=6.](https://tex.z-dn.net/?f=9%3Dk%5Ctimes%5Cdfrac%7B3%7D%7B2%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20k%3D%5Cdfrac%7B18%7D%7B3%7D%5C%5C%5C%5C%5CRightarrow%20k%3D6.)
So, equation (i) becomes
![y=6x.](https://tex.z-dn.net/?f=y%3D6x.)
Therefore, when x = 1, we get
![y=6\times1=6.](https://tex.z-dn.net/?f=y%3D6%5Ctimes1%3D6.)
Thus, the required value of y is 6.