To write the equation \( y = \frac{1}{8}x + 7 \) in standard form using integers, we should rearrange it into the form \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers.
Start with the given equation:
\[ y = \frac{1}{8}x + 7 \]
Multiply every term by 8 to eliminate the fraction:
\[ 8y = x + 56 \]
Next, rearrange the equation to get \( x \) and \( y \) on the same side:
\[ -x + 8y = 56 \]
To convert it to standard form \( Ax + By = C \), we typically prefer \( A \) to be positive. So, we can multiply the entire equation by \(-1\):
\[ x - 8y = -56 \]
Therefore, the standard form of the equation is:
\[ x - 8y = -56 \]