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 that the slope \(m\) is \(\frac{1}{9}\) and the point is \((-4, -7)\), we can substitute these values into the formula.
Here, \(x_1 = -4\) and \(y_1 = -7\).
Substituting the values into the point-slope form:
\[ y - (-7) = \frac{1}{9}(x - (-4)) \]
This simplifies to:
\[ y + 7 = \frac{1}{9}(x + 4) \]
So, the equation of the line in point-slope form is:
\[ y + 7 = \frac{1}{9}(x + 4) \]