To complete the table for the equation \( y = \frac{1}{3}x + 7 \), we'll substitute the given values of \( x \) into the equation and solve for \( y \).
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For \( x = -6 \): \[ y = \frac{1}{3}(-6) + 7 = -2 + 7 = 5 \] Thus, when \( x = -6 \), \( y = 5 \).
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For \( x = 3 \): \[ y = \frac{1}{3}(3) + 7 = 1 + 7 = 8 \] Thus, when \( x = 3 \), \( y = 8 \).
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For \( x = 6 \): \[ y = \frac{1}{3}(6) + 7 = 2 + 7 = 9 \] Thus, when \( x = 6 \), \( y = 9 \).
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For \( x = 9 \): \[ y = \frac{1}{3}(9) + 7 = 3 + 7 = 10 \] Thus, when \( x = 9 \), \( y = 10 \).
Now we can summarize the completed table:
| \( x \) | \( y \) | |:---------:|:---------:| | -6 | 5 | | 3 | 8 | | 6 | 9 | | 9 | 10 |