To fill in the missing values in the table using the equation \( y - 6 = \frac{x}{4} \), we can first rearrange this equation to solve for \( y \):
\[ y = \frac{x}{4} + 6 \]
Now, we can use this equation to calculate the missing values in the table for each given \( x \) value.
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When \( x = 32 \): \[ y = \frac{32}{4} + 6 = 8 + 6 = 14 \] (This is already filled in.)
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When \( x = 12 \): \[ y = \frac{12}{4} + 6 = 3 + 6 = 9 \]
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When \( x = 0 \): \[ y = \frac{0}{4} + 6 = 0 + 6 = 6 \]
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When \( y = 4 \): We need to find \( x \). \[ 4 - 6 = \frac{x}{4} \] \[ -2 = \frac{x}{4} \] \[ x = -8 \]
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When \( y = -3 \): Again, we need to find \( x \). \[ -3 - 6 = \frac{x}{4} \] \[ -9 = \frac{x}{4} \] \[ x = -36 \]
Now, we can fill in the table with the calculated values:
\[ \begin{array}{|c|c|} \hline x & y \ \hline 32 & 14 \ 12 & 9 \ 0 & 6 \ -8 & 4 \ -36 & -3 \ \hline \end{array} \]
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