To find the slope of a line that is perpendicular to the line given by the equation \(x + y = 9\), we first need to determine the slope of the given line.
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Rearrange the equation into slope-intercept form \(y = mx + b\), where \(m\) is the slope: \[ x + y = 9 \] Subtract \(x\) from both sides: \[ y = -x + 9 \] From this, we can see that the slope \(m\) of the line is \(-1\).
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Find the slope of the perpendicular line. The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. The negative reciprocal of \(-1\) is: \[ \text{Perpendicular slope} = -\frac{1}{-1} = 1 \]
Thus, the slope of a line perpendicular to the line whose equation is \(x + y = 9\) is \(\boxed{1}\).
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