To write the equation of a line in point-slope form, we use the formula:
\[ y - y_1 = m(x - x_1) \]
where \(m\) is the slope and \((x_1, y_1)\) is a point on the line.
Here, the slope \(m = \frac{1}{2}\) and the point \((x_1, y_1) = (1, 5)\).
Substituting these values into the formula gives:
\[ y - 5 = \frac{1}{2}(x - 1) \]
This is the equation of the line in point-slope form.