To find which table might represent Ava's line based on her expression \(4 - 12 - 3\), we first need to simplify that expression:
\[ 4 - 12 - 3 = 4 - 15 = -11 \]
It seems like Ava might be calculating the slope of a line in the form \(y = mx + b\), where \(m\) is the slope. However, the given calculation results in a numerical value (-11) that seems not to directly correspond to the slope between any two points.
To determine the slope from a table of values \( (x, y) \), we can calculate the slope \(m\) between two points using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's analyze each given table to determine the slopes:
For the first table:
\[ \begin{align*} (3, 1) \quad & (2, 4) \ \end{align*} \]
Calculating the slope: \[ m = \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3 \]
For the second table:
\[ \begin{align*} (4, 3) \quad & (2, 1) \ \end{align*} \]
Calculating the slope: \[ m = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \]
For the third table:
\[ \begin{align*} (3, 4) \quad & (-1, -2) \ \end{align*} \]
Calculating the slope: \[ m = \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2} \]
For the fourth table:
\[ \begin{align*} (4, 3) \quad & (2, 1) \ \end{align*} \]
Calculating the slope: \[ m = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \]
From these calculations, none of the slopes (-3, 1, 3/2, 1) match the value of -11, which suggests a misunderstanding about the relationship between the slope and the given tables.
Since we are interested in the possibility that one of these tables represents a line that potentially has a slope calculated (or implying a slope) from Ava's expression, we focus on identifying the nature of the table data instead.
The expression itself - if intended to be a slope of -11 - would indicate a decline, and typically such steeper slopes would correspond to larger absolute changes in \(y\) for comparable changes in \(x\), suggesting incorrect or misunderstood match-up between what was calculated and these tables of simple coordinate points.
For further assistance, one might need to clarify the intention behind the expression and its relation to these tables or correct calculation processes as none directly link clearly. Could you clarify or provide more information about Ava's line?