Write each equation in standard form using integers

The idea is to get the equation into the form Ax+By = C
where A,B and C are integers

So we subtract x from both sides
y = x+6
y-x = x+6-x
-x+y = 6

Then multiply both sides by -1 to make the value of A positive
-x+y = 6
-1*(-x+y) = -1*6
x-y = -6

So the final answer is:  x - y = -6