To determine which table might represent Ava's line based on the expression \( 4 - 12 - 3 \), we first need to simplify the expression:
\[ 4 - 12 - 3 = 4 - 15 = -11 \]
This expression does not directly relate to the slope of a line unless we consider the numbers individually. However, if we interpret the operation as representing a slope, we can compute the slope from two points in a table.
The slope formula is given by:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Since Ava's expression evaluates to -11, we'll look for pairs of (x, y) that have a slope of -11.
Now let's analyze the response options:
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Table: \[ \begin{array}{c|c} x & y \ \hline 4 & 3 \ 2 & 1 \ \end{array} \]
- Slope Calculation: \[ \text{slope} = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \quad (\text{Not } -11) \]
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Table: \[ \begin{array}{c|c} x & y \ \hline 3 & 4 \ -1 & -2 \ \end{array} \]
- Slope Calculation: \[ \text{slope} = \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2} \quad (\text{Not } -11) \]
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Table: \[ \begin{array}{c|c} x & y \ \hline 4 & 3 \ 2 & 1 \ \end{array} \]
(This is the same as the first table.)
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Table: \[ \begin{array}{c|c} x & y \ \hline 3 & 1 \ 2 & 4 \ \end{array} \]
- Slope Calculation: \[ \text{slope} = \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3 \quad (\text{Not } -11) \]
Based on the provided choices, none give a slope of -11, which would require examining points specifically for this slope.
Thus, Ava might need to choose a table that yields a slope of -11 or apply her calculations to find the corresponding values.
Assuming your inquiry aims at determining a table from those options, the tables presented do not yield a slope of -11. Therefore, if she was looking for one that represents the necessary slope, none match this criteria directly.
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