1. **State the problem:** We need to write the equation of a line in point-slope form that passes through the point $(-6,4)$ and has a slope of $-\frac{4}{3}$. 2. **Recall the point-slope form:** The point-slope form of a line is given by: $$y - y_1 = m(x - x_1)$$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line. 3. **Substitute the given values:** Here, $m = -\frac{4}{3}$, $x_1 = -6$, and $y_1 = 4$. Substitute these into the formula: $$y - 4 = -\frac{4}{3}(x - (-6))$$ which simplifies to $$y - 4 = -\frac{4}{3}(x + 6)$$ 4. **Final answer:** The equation of the line in point-slope form is: $$\boxed{y - 4 = -\frac{4}{3}(x + 6)}$$