A ray of light travels along the line $2x-3y+5=0$  and strikes a plane mirror lying along the line $x+y=2$ The equation of the straight line containing the reflected ray is 

Let $\theta$  be the angle which the ray  $2x-3y+5$ $\models 0$

makes with the line $x+y=2$  then  $\theta =\left|\frac{2/3+1}{1-2/3\left(1\right)}\right|$ 

$=\left|5\right|=5$  

Reffected ray makes angle $-\theta$ with $x+y=2$ so if the slope

of the reflected ray is m then $\frac{m+1}{1-m}=\tan (-\theta )=-5$

               $\Rightarrow m=3/2\text{. }$

Also, the reflected ray passes through  $(1/5,9/5)$ the point of 

intersection of the ray and the line
Hence equation of the reflected ray is

$\begin{array}{l}(y-9/5)=3/2(x-1/5)\\ \Rightarrow 3x-2y+3=0\end{array}$