To find the slope of a line parallel to the given line \(5x + 2y = 6\), we first need to determine the slope of the original line.
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Start by rewriting the equation in slope-intercept form (y = mx + b), where \(m\) is the slope.
Begin with the original equation: \[ 5x + 2y = 6 \]
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Solve for \(y\): \[ 2y = -5x + 6 \] \[ y = -\frac{5}{2}x + 3 \]
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From the equation \(y = -\frac{5}{2}x + 3\), we see that the slope \(m\) of the line is \(-\frac{5}{2}\).
Since parallel lines have the same slope, the slope of a line parallel to the given line is also \(-\frac{5}{2}\).
Thus, the slope of a line parallel to \(5x + 2y = 6\) is \(\boxed{-\frac{5}{2}}\).