Step 1 :Given the slope \(m = -\frac{1}{2}\) and the point \((4,9)\) through which the line passes.
Step 2 :Substitute the given values into the point-slope form equation \(y - y_1 = m(x - x_1)\).
Step 3 :Substituting \(m = -\frac{1}{2}\), \(x_1 = 4\), and \(y_1 = 9\) into the point-slope form equation, we get:
Step 4 :\(y - 9 = -\frac{1}{2}(x - 4)\)
Step 5 :So, the point-slope form of the line is \(\boxed{y - 9 = -\frac{1}{2}(x - 4)}\).