Find the slope and $y$-intercept of the following linear equation. Express the $y$-intercept as a coordinate pair.
\[
6 x+4 y=5
\]

Step 1 ：The given equation is in the standard form of a linear equation, which is \(Ax + By = C\). To find the slope and y-intercept, we need to convert this equation into slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 2 ：To do this, we can rearrange the equation to solve for \(y\).

Step 3 ：\(6x + 4y = 5\) can be rearranged to \(y = \frac{5}{4} - \frac{3}{2}x\).

Step 4 ：The slope of the line is \(-\frac{3}{2}\) and the y-intercept is \(\frac{5}{4}\). The y-intercept as a coordinate pair would be \((0, \frac{5}{4})\).

Step 5 ：Final Answer: The slope of the line is \(\boxed{-\frac{3}{2}}\) and the y-intercept is \(\boxed{\left(0, \frac{5}{4}\right)}\).