To determine which table might represent Ava's line using the expression \(4 - 12 - 3\), we first need to evaluate the expression.
Simplifying it:
\[ 4 - 12 - 3 = 4 - 15 = -11. \]
However, this expression might be incorrectly interpreted or miscommunicated. Instead, if we assume Ava is trying to find the slope of a line defined by two points (for example, using the points at (4, 3) and (2, 1)), we can calculate the slope using the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1}. \]
Let's calculate the slope for the first table:
For the first table:
Points: (4, 3) and (2, 1)
\[ \text{slope} = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1. \]
For the second table:
Points: (3, 1) and (2, 4)
\[ \text{slope} = \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3. \]
For the third table:
Same as the first table, so it will also yield a slope of 1.
For the fourth table:
Points: (3, 4) and (-1, -2)
\[ \text{slope} = \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2}. \]
Summarizing:
- The first and third tables yield a slope of 1.
- The second table yields a slope of -3.
- The fourth table yields a slope of \( \frac{3}{2} \).
Ava likely determined the slope using the standard slope formula, which means the table with points yielding the slope of 1 (either the first or third table) would align best with her expression.
Therefore, the correct response is:
The first table:
x | y --|-- 4 | 3 2 | 1