The Solution.
The slope of line BC is given below:
[tex]\begin{gathered} \text{slope = }\frac{y_2-y_1}{x_2-x_1} \\ B(1,6)\rightarrow(x_1=1,y_1=6) \\ C(4,0)\rightarrow(x_2=4,y_2=0) \end{gathered}[/tex]Substituting the values above into the formula, we get
[tex]\text{Slope = }\frac{0-6}{4-1}=-\frac{6}{3}=-2[/tex]Thus, the correct answer is -2.