A line passing through the point A ( 9 , 0 ) makes an angle of 30 ° with the positive direction of x -axis.…

Given,

A straight line passes through $A\left(9,0\right)$ and makes a angle ${30}^{°}$ with the $x-$axis,

And it is rotated by ${15}^{°}$ degree clockwise

So, the new angle with the $x-$axis will be $\theta ={30}^{°}-{15}^{°}={15}^{°}$

Hence, the equation of the line will be,

$y-0=\tan {15}^{°}\left(x-9\right)$

$\Rightarrow y=\tan \left({45}^{°}-{30}^{°}\right)\left(x-9\right)$

$\Rightarrow y=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}\left(x-9\right)$

$\Rightarrow y=\left(2-\sqrt{3}\right)\left(x-9\right)$