To find the slope of the linear function given by the equation \(10x + 2y = 6\), we can rearrange the equation into slope-intercept form, which is \(y = mx + b\), where \(m\) represents the slope.
Starting with the original equation:
\[ 10x + 2y = 6 \]
We can isolate \(y\) by following these steps:
- Subtract \(10x\) from both sides:
\[ 2y = -10x + 6 \]
- Divide every term by \(2\) to solve for \(y\):
\[ y = -5x + 3 \]
Now, the equation is in slope-intercept form \(y = mx + b\), where \(m = -5\) and \(b = 3\).
Thus, the slope of the linear function is
\[ \boxed{-5}. \]