To determine which of the given tables represent a linear function with the same slope as \( y = 2 - 3x \), we first need to establish the slope of the given equation.
The equation \( y = 2 - 3x \) can be rewritten as \( y = -3x + 2 \). From this, we can see that the slope (m) is \(-3\).
Next, we'll calculate the slopes of the linear relationships represented by each table.
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Table 1:
- \(x = 0, y = 10\)
- \(x = 1, y = 7\) → Slope = \( \frac{7-10}{1-0} = \frac{-3}{1} = -3 \)
- \(x = 2, y = 4\) → Slope = \( \frac{4-7}{2-1} = \frac{-3}{1} = -3 \)
- \(x = 3, y = 1\) → Slope = \( \frac{1-4}{3-2} = \frac{-3}{1} = -3 \)
- \(x = 4, y = -2\) → Slope = \( \frac{-2-1}{4-3} = \frac{-3}{1} = -3 \)
- Slope = -3 (Matches)
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Table 2:
- \(x = 2, y = 4\)
- \(x = 4, y = 10\) → Slope = \( \frac{10-4}{4-2} = \frac{6}{2} = 3 \)
- Slope ≠ -3 (Doesn't match)
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Table 3:
- \(x = 2, y = 25\)
- \(x = 4, y = 19\) → Slope = \( \frac{19-25}{4-2} = \frac{-6}{2} = -3 \)
- \(x = 6, y = 13\) → Slope = \( \frac{13-19}{6-4} = \frac{-6}{2} = -3 \)
- \(x = 8, y = 7\) → Slope = \( \frac{7-13}{8-6} = \frac{-6}{2} = -3 \)
- \(x = 10, y = 1\) → Slope = \( \frac{1-7}{10-8} = \frac{-6}{2} = -3 \)
- Slope = -3 (Matches)
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Table 4:
- \(x = 0, y = 2\)
- \(x = 1, y = 5\) → Slope = \( \frac{5-2}{1-0} = \frac{3}{1} = 3 \)
- Slope ≠ -3 (Doesn't match)
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Table 5:
- \(x = 0, y = 2\)
- \(x = 1, y = 4\) → Slope = \( \frac{4-2}{1-0} = \frac{2}{1} = 2 \)
- Slope ≠ -3 (Doesn't match)
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Table 6:
- \(x = 2, y = 10\)
- \(x = 4, y = 8\) → Slope = \( \frac{8-10}{4-2} = \frac{-2}{2} = -1 \)
- Slope ≠ -3 (Doesn't match)
Conclusion:
The tables that represent a linear function with the same slope as \( y = 2 - 3x \) are:
- Table 1
- Table 3
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