1. **State the problem:** Find the equation of the line passing through the point $(3,1)$ with slope $m = -\frac{4}{3}$.\n\n2. **Formula used:** The point-slope form of a line is given by $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope.\n\n3. **Substitute the known values:** Here, $x_1 = 3$, $y_1 = 1$, and $m = -\frac{4}{3}$. So, $$y - 1 = -\frac{4}{3}(x - 3)$$\n\n4. **Simplify the equation:** Distribute the slope on the right side: $$y - 1 = -\frac{4}{3}x + 4$$\n\n5. **Isolate $y$ to get slope-intercept form:** Add 1 to both sides: $$y = -\frac{4}{3}x + 4 + 1$$\n$$y = -\frac{4}{3}x + 5$$\n\n**Final answer:** The equation of the line is $$y = -\frac{4}{3}x + 5$$