To write the equation \( y = x + 7 \) in standard form using integers, we want it in the format \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers and \( A \) is non-negative.
Starting with the original equation:
\[ y = x + 7 \]
To rearrange this into standard form, we can subtract \( x \) from both sides:
\[ -y + x = 7 \]
Next, we can rewrite it as:
\[ x - y = 7 \]
Now, this is in the standard form \( Ax + By = C \) where \( A = 1 \), \( B = -1 \), and \( C = 7 \).
Thus, the equation in standard form is:
\[ x - y = 7 \]