To determine which table might represent Ava's line based on the expression \(4 - \frac{1}{2} - 3\), we first need to simplify the expression.
Calculating the expression: \[ 4 - \frac{1}{2} - 3 = 4 - 0.5 - 3 = 0.5 \]
This means that the slope of the line Ava is considering is \(0.5\) (or \(\frac{1}{2}\)).
Now, a slope of \(\frac{1}{2}\) means that for every 2 units you go up in the \(y\)-direction, you go 1 unit in the \(x\)-direction, or, equivalently, for every decrease in \(x\), there should be a corresponding increase in \(y\) consistent with that slope.
Let’s evaluate each table to see which has a slope of \(0.5\) or \(\frac{1}{2}\):
Option a:
- Points (4, 3) and (2, 1)
- Slope \(= \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1\)
Option b:
- Points (3, 1) and (2, 4)
- Slope \(= \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3\)
Option c:
- Points (3, 4) and (-1, -2)
- Slope \(= \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2}\)
Option d:
- Points (4, 3) and (2, 1)
- Slope \(= \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1\)
None of the provided tables show a slope of \(0.5\). However, Option A and Option D contain the same pairs of points which provide a slope of \(1\), while the other response options give different slopes.
We may have made a mistake in the slope evaluations; let's look for pairs overall with the condition of forming a relationship consistent with \(0.5\). So, if we want a slope of \(0.5\), we know it would imply specific arrangements.
However, based on the pairs provided in the tables, none fit the slope of \(0.5\).
Do review the expression again and confirm, or check for slight adjustments leading you back to ensure the expected slope represents a fraction of corresponding unit movements concluding.
In conclusion, the tables listed do not represent an accurate match for a slope of \(0.5\), implying an inquiry around correctness or numerical definitions may be a step to take further.
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