To determine which table might represent Ava's line, we first need to clarify the expression Ava wrote, which is \(4 - 12 - 3\). This expression simplifies to:
\[ 4 - 12 - 3 = 4 - 15 = -11 \]
However, it seems more likely that Ava intended to find the slope of the line, potentially using a different set of numbers or context. To find the slope (m), we need two points from the tables and then calculate the slope using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Now, let's analyze the tables provided to see if any of them represent lines with a consistent slope:
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Table 1: \[ \begin{array}{c|c} x & y \ \hline 3 & 1 \ 2 & 4 \ \end{array} \]
- Slope calculation: \[ m = \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3 \]
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Table 2: \[ \begin{array}{c|c} x & y \ \hline 3 & 4 \ -1 & -2 \ \end{array} \]
- Slope calculation: \[ m = \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2} \]
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Table 3: (same as Table 4) \[ \begin{array}{c|c} x & y \ \hline 4 & 3 \ 2 & 1 \ \end{array} \]
- Slope calculation: \[ m = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \]
Now let's recap the slopes we calculated for the tables:
- Table 1: slope of -3
- Table 2: slope of \( \frac{3}{2} \)
- Table 3 and 4: slope of 1
Given that the slope was determined in the context of \(4 - 12 - 3\) resulting in -11 and was likely part of a different exercise, the most consistent representation of a line might be with the slope of -3 (as negative slopes could relate to a downward trend).
If your question was specifically about which of the tables could be related to a slope based on Ava's expression, normally we would be looking for either negative or positive slopes depending on her earlier calculations. From the choices available without additional clarifying criteria, Table 1 would have a consistent downward slope (negative slope).
So, the answer may be interpreted based on the context, but if focusing strictly on slopes derived from the tables: Table 1 could represent a line that relates to a negative slope.
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