To find the values of \( y \) for the equation \( 4y = -x + 12 \) given the values of \( x \) (which are -8, -4, 0, 4, and 8), we need to first rewrite the equation in terms of \( y \):
\[ y = \frac{-x + 12}{4} = -\frac{1}{4}x + 3 \]
Now we can calculate \( y \) for each given \( x \) value.
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For \( x = -8 \): \[ y = -\frac{1}{4}(-8) + 3 = 2 + 3 = 5 \]
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For \( x = -4 \): \[ y = -\frac{1}{4}(-4) + 3 = 1 + 3 = 4 \]
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For \( x = 0 \): \[ y = -\frac{1}{4}(0) + 3 = 0 + 3 = 3 \]
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For \( x = 4 \): \[ y = -\frac{1}{4}(4) + 3 = -1 + 3 = 2 \]
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For \( x = 8 \): \[ y = -\frac{1}{4}(8) + 3 = -2 + 3 = 1 \]
Now we can summarize the results:
\[ \begin{align*} x = -8 & \rightarrow y = 5 \ x = -4 & \rightarrow y = 4 \ x = 0 & \rightarrow y = 3 \ x = 4 & \rightarrow y = 2 \ x = 8 & \rightarrow y = 1 \ \end{align*} \]
So the corresponding values of \( (x, y) \) pairs would be:
\[ (-8, 5), (-4, 4), (0, 3), (4, 2), (8, 1) \]