To find the slope of a line, we can use the formula:
\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]
From Ava's expression \(5 - 14 - 2\), we can simplify it:
\[ 5 - 14 = -9 \] \[ -9 - 2 = -11 \]
This suggests that the slope \(m = -11\).
Now we'll determine which table of values might represent a slope of -11.
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First table:
- Points: (2, 5) and (4, 1)
- Slope calculation: \[ m = \frac{1 - 5}{4 - 2} = \frac{-4}{2} = -2 \]
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Second table:
- Points: (5, 4) and (1, 2)
- Slope calculation: \[ m = \frac{2 - 4}{1 - 5} = \frac{-2}{-4} = \frac{1}{2} \]
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Third table:
- Points: (4, -5) and (2, -1)
- Slope calculation: \[ m = \frac{-1 - (-5)}{2 - 4} = \frac{4}{-2} = -2 \]
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Fourth table:
- Points: (2, 1) and (4, 5)
- Slope calculation: \[ m = \frac{5 - 1}{4 - 2} = \frac{4}{2} = 2 \]
None of the tables calculated have a slope of -11.
If there are no other tables to choose from, the mistake could be in the interpretation of Ava’s expression or the tables provided.
Based on the calculated slopes, none of the options represent a slope of -11. Please check if there were any errors in the formulation of the problem or the choices given.
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