\[ y = 15 - {x + 3 \over 2} = 15 - \left({x \over 2} + {3 \over 2}\right) = 15 - {1 \over 2}\,x - {3 \over 2} \]
\[ y\,' = 0 - {1 \over 2} - 0 = - {1 \over 2} \]