Basic Differential Eqn - initial value problem

[Zem]

The equation starts with dy/dt = ay - b, and initial condition y(0) = y_o and y_o is an arbitrary value. The book says this can be rewritten as:
(dy/dt)/[y - (b/a)] = a. But I don't see how do make that step algebraically. How can the original be rewritten like that?

A problem at the end of the chapter appears to be designed to use the above equation.
(dy/dt) = -y + 5

Am I correct in assuming I should rewrite it as this?
(dy/dt)/[y - 5/(-1)] = -1

Then follow the steps to solve that? Beginning with:
(ln[y - (5/(-1)]) = -1t + C

 

[dicerandom]

For the first step, factor an a out of the right hand side then divide both sides by (y-b/a).