Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form $y=m x+b$.
\[
(6,8) ; x+6 y=5
\]
The equation of the line is (Type an equation. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Simplify your answer.)

Step 1 ：The given line is in the form \(ax + by = c\). We can convert it to the slope-intercept form \(y = mx + b\) by isolating \(y\).

Step 2 ：The slope of the line parallel to this line would be the same.

Step 3 ：We can then use the point-slope form of the line \(y - y_1 = m(x - x_1)\) to find the equation of the line passing through the given point and parallel to the given line.

Step 4 ：The given line is \(x + 6y = 5\).

Step 5 ：Converting it to slope-intercept form, we get \(y = -\frac{1}{6}x + \frac{5}{6}\).

Step 6 ：So, the slope \(m\) of the line parallel to this line is \(-\frac{1}{6}\).

Step 7 ：Using the point-slope form of the line with the given point \((6,8)\), we get \(y - 8 = -\frac{1}{6}(x - 6)\).

Step 8 ：Solving for \(y\), we get \(y = -\frac{1}{6}x + 9\).

Step 9 ：This is in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 10 ：Final Answer: The equation of the line is \(\boxed{y = -\frac{1}{6}x + 9}\).