To determine whether the point \( (x, y) = (-2, -\frac{2}{3}) \) satisfies the equation \( y = -\frac{5}{9}x - \frac{16}{9} \), we can substitute \( x = -2 \) into the equation and see if it yields \( y = -\frac{2}{3} \).
Substituting \( x = -2 \):
\[ y = -\frac{5}{9}(-2) - \frac{16}{9} \]
Calculating \( -\frac{5}{9}(-2) \):
\[ -\frac{5}{9} \times -2 = \frac{10}{9} \]
Now substituting back into the equation:
\[ y = \frac{10}{9} - \frac{16}{9} \]
Calculating \( \frac{10}{9} - \frac{16}{9} \):
\[ y = \frac{10 - 16}{9} = \frac{-6}{9} = -\frac{2}{3} \]
Since we calculated \( y \) as \( -\frac{2}{3} \), the point \( (x, y) = (-2, -\frac{2}{3}) \) does satisfy the equation \( y = -\frac{5}{9}x - \frac{16}{9} \).
Thus, the solution is confirmed:
\[ y = -\frac{2}{3} \quad \text{when} \quad x = -2 \]
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