To determine the slope of a line based on Ava's expression \(5 - 14 - 2\), we can first simplify it.
The expression simplifies as follows:
\[ 5 - 14 - 2 = 5 - 16 = -11 \]
This means the slope of Ava's line is \(-11\).
Now, we can look for a table of values for which the slope between any two points is \(-11\). The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
For the slope to be \(-11\), the change in \(y\) must be \(-11\) times the change in \(x\). Therefore, for any two points:
\[ y_2 - y_1 = -11(x_2 - x_1) \]
Let's analyze the provided responses for their slopes:
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For the first table:
- \( (2, 5) \) and \( (4, 1) \)
- Slope calculation: \(\frac{1 - 5}{4 - 2} = \frac{-4}{2} = -2\)
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For the second table:
- The values are the same as the first table, so the slope is also \(-2\).
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For the third table:
- \( (5, 4) \) and \( (1, 2) \)
- Slope calculation: \(\frac{2 - 4}{1 - 5} = \frac{-2}{-4} = \frac{1}{2}\)
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For the fourth table:
- Values are again the same as the third table, so the slope remains \(\frac{1}{2}\).
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For the fifth table:
- \( (4, -5) \) and \( (2, -1) \)
- Slope calculation: \(\frac{-1 + 5}{2 - 4} = \frac{4}{-2} = -2\)
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For the sixth table:
- Values are again the same as the fifth table, so the slope is \(-2\).
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For the seventh table:
- This involves points \( (2, 1) \) and \( (4, 5) \).
- Slope calculation: \(\frac{5 - 1}{4 - 2} = \frac{4}{2} = 2\)
After calculating all the slopes, none of the tables produce a slope of \(-11\). Therefore, there appears to be no suitable answer given in the responses that matches the slope calculated from Ava's expression. It looks like Ava's calculation doesn’t correspond to any of the tables provided.
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