To complete the table for the equation \(-x + 9y = 9\), we'll solve for \(y\) in terms of \(x\).
Starting with the equation:
\[ -x + 9y = 9 \]
Rearranging gives:
\[ 9y = x + 9 \]
Now, dividing both sides by 9:
\[ y = \frac{x + 9}{9} = \frac{x}{9} + 1 \]
Now we can calculate \(y\) for each given value of \(x\):
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For \(x = 9\): \[ y = \frac{9}{9} + 1 = 1 + 1 = 2 \]
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For \(x = 18\): \[ y = \frac{18}{9} + 1 = 2 + 1 = 3 \]
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For \(x = 27\): \[ y = \frac{27}{9} + 1 = 3 + 1 = 4 \]
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For \(x = 36\): \[ y = \frac{36}{9} + 1 = 4 + 1 = 5 \]
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For \(x = 45\): \[ y = \frac{45}{9} + 1 = 5 + 1 = 6 \]
Now, we can fill in the table:
\[ \begin{array}{|c|c|} \hline x & y \ \hline 9 & 2 \ 18 & 3 \ 27 & 4 \ 36 & 5 \ 45 & 6 \ \hline \end{array} \]
This completes the table with the corresponding values of \(y\) for each \(x\).