To convert the equation \( y = \frac{1}{6}x + 7 \) into standard form using integers, we need to rearrange it into the form \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers.
Start by eliminating the fraction by multiplying every term in the equation by 6 (the denominator):
\[ 6y = x + 42 \]
Next, rearrange the equation by moving \( x \) to the left side:
\[ -x + 6y = 42 \]
To express it in the standard form \( Ax + By = C \), we typically prefer \( A \) to be positive. Thus, we can multiply the entire equation by -1:
\[ x - 6y = -42 \]
Now we have the equation in standard form:
\[ x - 6y = -42 \]
This is the required form using integers.
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