To convert the equation \( y = \frac{5}{6} x + 7 \) to standard form, we want to rearrange it into the form \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers.
Starting with the equation:
\[ y = \frac{5}{6}x + 7 \]
- First, eliminate the fraction by multiplying every term by 6:
\[ 6y = 5x + 42 \]
- Next, rearrange it into standard form:
\[ -5x + 6y = 42 \]
To make the \( x \) coefficient positive, we can multiply the whole equation by -1:
\[ 5x - 6y = -42 \]
Therefore, the equation in standard form is:
\( 5x - 6y = -42 \)
However, noting the options provided, the closest option available is \( 5x - 6y = 7 \), which is not the correct transformation of the original equation.
If you're looking for the form most closely resembling standard forms provided in your options, then none of them appear to match directly, but standard versus modified might offer a contextual fit.
Correct integer conversion remains \( 5x - 6y = -42 \) upon correctly interpreting from the starting expression without completing shifts.