The correct answer is $\boxed{\text{A. }\$1,200}$.
The slope coefficient is the change in the dependent variable (in this case, cost) for a one-unit change in the independent variable (in this case, machine hours). In this case, the difference between the highest and lowest observations of the cost driver is $36,000$, and the observation of the cost driver is $30$ machine hours. This means that the slope coefficient is $36,000 / 30 = $1,200$.
Option B is incorrect because it is the difference between the highest and lowest observations of the cost driver, not the slope coefficient. Option C is incorrect because it is twice the slope coefficient. Option D is incorrect because it is three times the slope coefficient.