The function is linear, thus 2 point shall determine it.

f(1)=3.

Thus, (1,3) is a point on the line.

By condition 2 we have:

f(1) = f(2) -2

Thus,

3=f(2)-2

Thus,

f(2)=5

Hence,

(2,5) is a point on the line.

Now you have two points you can find the equation of the line.