Answer: $10.5$

Explanation:1. Simplify the given equation to the slope-intercept form ($y=mx+b$): The equation is $y=\dfrac{1}{2}(15x+12)+3x$. First, distribute $\dfrac{1}{2}$ to the terms inside the parenthesis: $y = \dfrac{1}{2}(15x) + \dfrac{1}{2}(12) + 3x$ $y = \dfrac{15}{2}x + \dfrac{12}{2} + 3x$ $y = \dfrac{15}{2}x + 6 + 3x$

2. Combine the terms containing x: To combine $\dfrac{15}{2}x$ and $3x$, write $3x$ as $\dfrac{6}{2}x$. $y = (\dfrac{15}{2} + \dfrac{6}{2})x + 6$ $y = \dfrac{15+6}{2}x + 6$ $y = \dfrac{21}{2}x + 6$

3. Identify the slope: The equation is now in the slope-intercept form $y=mx+b$, where m is the slope. The slope $m = \dfrac{21}{2}$.

4. Convert the slope to a decimal: $m = \dfrac{21}{2} = 10.5$.

5. State the answer: The slope of the graph is $10.5$.

6. Conclusion: The slope of the graph of $y=\dfrac{1}{2}(15x+12)+3x$ in the xy-plane is $10.5$.