Step 1 :The equation of a line in slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Step 2 :We are given the slope \(m = \frac{1}{3}\) and a point \((x_1, y_1) = (6, 2)\). We can substitute these values into the equation to solve for \(b\).
Step 3 :Substituting the values, we get \(2 = \frac{1}{3} * 6 + b\). Solving for \(b\), we find that \(b = 0\).
Step 4 :Now that we have the y-intercept \(b = 0\), we can write the equation of the line.
Step 5 :\(\boxed{The equation of the line is y = \frac{1}{3}x + 0, or simply y = \frac{1}{3}x}\).