If you want it to be y=mx+b form then the equations should look like this: y=x+5 and y=-1/3x+1.
Any graph f(x) can be changed to f(x-3) by changing any x to x-3.
For example: Let f(x) = x^{2} + 2x + 4
Find f(x-3) by replacing all x's with x-3.
f(x-3) = (x - 3)^{2} + 2(x - 3) + 4
Then we can simplify and we will have f(x-3).