Writing an equation in function notation, with x as the independent variable is the same as solving the equation for y.
So, we start with
[tex]y-x-4=0[/tex]
and we move [tex]-x-4[/tex] to the right hand side, i.e. we add [tex]x+4[/tex] to both sides:
[tex]y-x-4+(x+4)=0+(x+4) \iff y=x+4[/tex]
