If the distance between parallel lines 3x + 4y +7 = 0 and ax + y + b = 0 is 1 , then sum of values of b is 

Since lines are parallel, we have $-\frac{3}{4}=-\frac{a}{1}$

$\Rightarrow a=\frac{3}{4}$

So, lines are 3x + 4y + 7 = 0 and 3x + 4y + 4b =0 Distance between lines = 1

$\begin{array}{r}\Rightarrow \frac{|7-4b|}{\sqrt{3^2+4^2}}=1\Rightarrow 7-4b=5 or 7-4b=-5\\ \\ \Rightarrow b=\frac{1}{2},3\end{array}$