Final answer:
The slope of the line representing the painting company's charges is $50 per hour of labor.
Step-by-step explanation:
The slope of the line that represents the cost to paint a house given by the painting company is obtained by identifying the rate of change in cost with respect to the hours of labor. In this scenario, the flat rate of $500 is the y-intercept, as this is the cost when no labor hours have been worked. The cost increases by $50 for each additional hour of labor, which means that $50 per hour is the slope of the line.