The given equation is: \[ y = -\frac{4}{5}x - 1 \]
To eliminate the fraction, multiply every term by 5: \[ 5y = -4x - 5 \]
Rearrange the terms to get the equation in the form \(Ax + By = C\): \[ 4x + 5y = -5 \]
The equation in standard form is: \[ \boxed{4x + 5y = -5} \]
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