To convert the equation \( y = \frac{1}{8}x + 7 \) to standard form using integers, we want to eliminate the fraction and rearrange the equation into the form \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers.
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Start with the original equation: \[ y = \frac{1}{8}x + 7 \]
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Multiply every term by 8 to eliminate the fraction: \[ 8y = x + 56 \]
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Rearrange the equation to standard form by moving \( x \) to the left side: \[ -x + 8y = 56 \]
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To make the coefficient of \( x \) positive, we can multiply the entire equation by -1: \[ x - 8y = -56 \]
Now the equation \( x - 8y = -56 \) is in standard form with integers.
Thus, the final answer is: \[ x - 8y = -56 \]