To write the equation of a line in point-slope form, we use the formula:
\[ y - y_1 = m(x - x_1) \]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.
Given the point \((4, 1)\) and a slope of \(-\frac{1}{9}\), we can substitute these values into the formula:
- \(x_1 = 4\)
- \(y_1 = 1\)
- \(m = -\frac{1}{9}\)
Substituting these values into the point-slope form gives us:
\[ y - 1 = -\frac{1}{9}(x - 4) \]
This is the equation of the line in point-slope form.