Rewrite y-3=3(x+1) in standard form

The standard from of a line has both variables on one side of the equal sign and a constant on the other side.  (by convention is should be arranged so that the coefficient of x is positive)

y-3=3(x+1)  perform indicated multiplication on right side

y-3=3x+3  subtract 3x from both sides

y-3x-3=3  add 3 to both sides

y-3x=6  multiply both sides by -1

3x-y=-6