To convert the equation \(-\frac{2}{3}x + y = -4\) into standard form, we want to express it in the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers and \(A\) is non-negative.
Starting from the given equation:
\[ -\frac{2}{3}x + y = -4 \]
- First, we can eliminate the fraction by multiplying every term by 3 (the denominator):
\[ 3 \left(-\frac{2}{3}x\right) + 3y = 3(-4) \]
This simplifies to:
\[ -2x + 3y = -12 \]
- To ensure \(A\) is non-negative, we can multiply the entire equation by -1:
\[ 2x - 3y = 12 \]
Now, the equation is in standard form, where \(A = 2\), \(B = -3\), and \(C = 12\):
\[ 2x - 3y = 12 \]