To find the slope of a line parallel to the line given by the equation \(5x + 2y = 6\), we first need to express this equation in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope.
Starting with the original equation:
\[ 5x + 2y = 6 \]
we isolate \(y\):
- Subtract \(5x\) from both sides:
\[ 2y = -5x + 6 \]
- Now divide every term by \(2\):
\[ y = -\frac{5}{2}x + 3 \]
From this equation, the slope \(m\) is \(-\frac{5}{2}\).
Since parallel lines have the same slope, the slope of a line parallel to the line given by \(5x + 2y = 6\) is also
\[ -\frac{5}{2}. \]