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