1. **State the problem:** Find the slope of the graph of the function $$y = \frac{1}{2} (11x + 16) + 4x$$ in the xy-plane. 2. **Recall the formula:** The slope of a linear function $$y = mx + b$$ is the coefficient $$m$$ of $$x$$. 3. **Simplify the given function:** $$y = \frac{1}{2} (11x + 16) + 4x = \frac{1}{2} \times 11x + \frac{1}{2} \times 16 + 4x = \frac{11}{2}x + 8 + 4x$$ 4. **Combine like terms:** $$y = \frac{11}{2}x + 4x + 8 = \frac{11}{2}x + \frac{8}{2}x + 8 = \left(\frac{11}{2} + \frac{8}{2}\right)x + 8 = \frac{19}{2}x + 8$$ 5. **Identify the slope:** The slope $$m$$ is the coefficient of $$x$$, which is $$\frac{19}{2}$$. 6. **Answer:** The slope of the graph is $$\frac{19}{2}$$, which corresponds to option B.