To find the slope of a line using Ava's expression \( 4 - 2 \cdot 3 - 1 \), we first need to simplify the expression.
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Perform the operations in order:
- Multiply \( 2 \cdot 3 = 6 \),
- Then the expression becomes \( 4 - 6 - 1 \).
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Now calculate:
- \( 4 - 6 = -2 \),
- \( -2 - 1 = -3 \).
Thus, the slope calculated from Ava's expression is \(-3\).
The slope of a line is defined as the change in y over the change in x (often represented as \( m = \frac{\Delta y}{\Delta x} \)). A slope of \(-3\) means that for every \( 1 \) unit increase in \( x \), \( y \) decreases by \( 3 \) units.
Now we can analyze the tables provided to identify which could represent a line with a slope of \(-3\):
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Table 1:
- \( (3, 4) \)
- \( (-1, -2) \)
- Change in y: \(-2 - 4 = -6\)
- Change in x: \(-1 - 3 = -4\)
- Slope: \(\frac{-6}{-4} = \frac{3}{2}\) (not \(-3\))
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Table 2:
- \( (4, 3) \)
- \( (2, 1) \)
- Change in y: \(1 - 3 = -2\)
- Change in x: \(2 - 4 = -2\)
- Slope: \(\frac{-2}{-2} = 1\) (not \(-3\))
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Table 3:
- \( (1, 2) \)
- \( (3, 4) \)
- Change in y: \(4 - 2 = 2\)
- Change in x: \(3 - 1 = 2\)
- Slope: \(\frac{2}{2} = 1\) (not \(-3\))
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Table 4:
- \( (1, 2) \)
- \( (2, 3) \)
- Change in y: \(3 - 2 = 1\)
- Change in x: \(2 - 1 = 1\)
- Slope: \(\frac{1}{1} = 1\) (not \(-3\))
No table appears to represent a line with a slope of \(-3\). Please ensure that the tables contain all the pairs that can be used to derive a slope of \(-3\). Given the choices listed, none of the provided tables represent a line with the correct slope of \(-3\).