Thanks to Mr Fantastic, I got the linear transformation of a simple exponential distribution. Now I'm trying to obtain the pdf of $\displaystyle Y= a X+b $. It looks cumbersome, is there any simpler methods? Where $\displaystyle X $ follows this Gamma distribution:

$\displaystyle f(x;k) = x^{k-1} \frac{e^{-x}}{\Gamma(k)}\text{ for } x > 0 $

Thank you.