To write the equation of the 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 the point the line passes through.
Given:
- Slope (\(m\)) = \( \frac{1}{9} \)
- Point (\(x_1, y_1\)) = \( (4, -7) \)
Now, substituting these values into the point-slope form equation:
\[ y - (-7) = \frac{1}{9}(x - 4) \]
This simplifies to:
\[ y + 7 = \frac{1}{9}(x - 4) \]
Therefore, the equation of the line in point-slope form is:
\[ y + 7 = \frac{1}{9}(x - 4) \]