Question

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 ?

Answer 1

For a perpendicular line, you use the negative reciprocal. Meaning if you wanted the perpendicular slope of 5/3 you would get -3/5. And the y-intercept is you last portion. Say your equation to a perpendicular line is y=-3/4x-7 and your y-intercept is 5 then your other equation would be y=4/3x+5.

Answer 2

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  =  - $\frac{1}{2}$

Thus equation would be y = - $\frac{1}{2}$ x  + 9