Step 1 :The equation of a line is given as \(y=\frac{2}{9} x+7\).
Step 2 :We are asked to find the slope of a line perpendicular to the given line.
Step 3 :The slope of a line perpendicular to a given line can be found by taking the negative reciprocal of the slope of the given line.
Step 4 :The slope of the given line is \(\frac{2}{9}\).
Step 5 :So, the slope of a line perpendicular to it is \(-\frac{1}{\frac{2}{9}}\).
Step 6 :Calculating the above expression, we get -4.5.
Step 7 :Thus, the slope of a line perpendicular to the given line is \(\boxed{-4.5}\).