How do you write the equation of a line if you know its y-intercept and the equation of a line to which it is perpendicular ?

if you are writing it in the form y = mx + c
  then you know that c it the y-intercept m the gardient

if you know the gradient of the peropendicular line then reciprocate that gradient and multiply it by  - 1 to get the gradient.

e.g.  gradient of perpen. = 2   and y intercept = 9
   
       then gradient of line  =  - 

Thus equation would be y = -  x  + 9