To find the slope of the line given by the equation \( y = (A + 1)x + 8 \) and that passes through the point \( (2, 6) \), we need to first substitute the coordinates of the point into the equation.
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Plug \( x = 2 \) and \( y = 6 \) into the line equation: \[ 6 = (A + 1) \cdot 2 + 8 \]
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Simplify the equation: \[ 6 = 2(A + 1) + 8 \] \[ 6 = 2A + 2 + 8 \] \[ 6 = 2A + 10 \]
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Rearranging the equation to find \( A \): \[ 6 - 10 = 2A \] \[ -4 = 2A \] \[ A = -2 \]
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Now substitute \( A \) back into the slope formula: The slope (\( m \)) of the line is given by \( m = A + 1 = -2 + 1 = -1 \).
Therefore, the slope of the line is \(\boxed{-1}\).
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