OK.. let me try..

Assume
q = mp + c   (i.e. linear function)   --- ( i)

for some other value of p and q say, p' and q ' , eqn (i) still holds .. i.e.
q' = mp' + c   ------ (ii)

But, if p increases by $5, q drops by 2 item, i.e.  for p' = p + 5, q' = q - 2.... with this eqn (ii) becomes,

q - 2 = mp + 5m + c  --- (iii)

Subract (i) from (iii)... and you get m = - 2/5 and put this value in eqn (i) to get

q = -2p/5 + c   ---- (iv)

Now, your task is to find the value of constant c.

But question says, would buy 100 itmes if price is $550 .. and what this means is:
p (i.e. price per item) = 550/100 = 5.5
q (i.e. quantity in demand) = 100

Now substitute these values of p and q in equation (iv), :

100 = -2 x 5.5/5 + c  ===> c = 102.2

Use this value in eqn (iv),
 
q = -2p/5 + 102.2    ..... this is the answer one...  q as a liner function of p.

from which,
p = -5q/2 + 102.2x5/2     (simplify it) .... this is answer to second question.. i.e. p as a liner function of q.

NOTE:  you should put complete question..

...
Disclaimer - it might be wrong... :)