To complete the table for the equation \( 4y = -x + 12 \), we need to solve for \( y \) in terms of \( x \):
- Rearranging the equation: \[ y = \frac{-x + 12}{4} = -\frac{x}{4} + 3 \]
Now we can calculate the values of \( y \) for each given value of \( x \):
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For \( x = -8 \): \[ y = -\frac{-8}{4} + 3 = 2 + 3 = 5 \]
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For \( x = -4 \): \[ y = -\frac{-4}{4} + 3 = 1 + 3 = 4 \]
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For \( x = 0 \): \[ y = -\frac{0}{4} + 3 = 0 + 3 = 3 \]
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For \( x = 4 \): \[ y = -\frac{4}{4} + 3 = -1 + 3 = 2 \]
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For \( x = 8 \): \[ y = -\frac{8}{4} + 3 = -2 + 3 = 1 \]
Now we can summarize the results in a table format:
\[ \begin{array}{|c|c|} \hline x & y \ \hline -8 & 5 \ -4 & 4 \ 0 & 3 \ 4 & 2 \ 8 & 1 \ \hline \end{array} \]
So the completed table is:
\[ \begin{array}{|c|c|} \hline x & y \ \hline -8 & 5 \ -4 & 4 \ 0 & 3 \ 4 & 2 \ 8 & 1 \ \hline \end{array} \]