To fill in the missing values in the table using the equation \( Y - 5 = \frac{x}{3} \), we can rearrange the equation to express \( Y \) in terms of \( x \):
\[ Y = \frac{x}{3} + 5 \]
Now we can calculate \( Y \) for each \( x \) value provided in the table and also fill in any missing \( x \) values when \( Y \) is known.
Given Entries:
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When \( x = - \) and \( Y = 1 \): \[ 1 = \frac{x}{3} + 5 \implies \frac{x}{3} = 1 - 5 \implies \frac{x}{3} = -4 \implies x = -12 \] So, \( x = -12 \)
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When \( x = -3 \) and \( Y = 4 \): \[ 4 = \frac{-3}{3} + 5 \implies 4 = -1 + 5 \implies 4 = 4 \quad \text{(This is already correct)} \]
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When \( x = 0 \) and \( Y = - \): \[ Y = \frac{0}{3} + 5 = 0 + 5 = 5 \] So, \( Y = 5 \)
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When \( x = 6 \) and \( Y = - \): \[ Y = \frac{6}{3} + 5 = 2 + 5 = 7 \] So, \( Y = 7 \)
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When \( x = - \) and \( Y = 8 \): \[ 8 = \frac{x}{3} + 5 \implies \frac{x}{3} = 8 - 5 \implies \frac{x}{3} = 3 \implies x = 9 \] So, \( x = 9 \)
Final Table:
Now we can summarize the completed table:
| X | Y | |-----|-----| | -12 | 1 | | -3 | 4 | | 0 | 5 | | 6 | 7 | | 9 | 8 |
The missing values have been filled in as specified.