Final answer:
In high school mathematics, the use of demand equations like p = - 8x + 800 is key to understanding price and quantity relationships in economics. These relationships can also be visualized using graphs that plot demand and supply curves to find the equilibrium price and quantity.
Step-by-step explanation:
The price p (in dollars) and the quantity x sold of a certain product satisfy the demand equation p = - 8x + 800. This is an example of how demand equations can be used to determine the relationship between price and quantity demanded of a product. In the context provided, solving this equation can tell us how many units would be sold at different price points, which is critical for understanding market dynamics.
Solving models with graphs is another method that can be used when working with such equations. Demand and supply curves can be plotted on a graph where the price (P) is on the vertical axis and the quantity (Qd for demand, Qs for supply) is on the horizontal axis. The intersection point of these curves will indicate the equilibrium price and quantity.
For example, with the demand curve P = 8 - 0.5Qd and supply curve P = -0.4 + 0.2Qs, careful plotting reveals the equilibrium to be at a price of $2 and a quantity of 12. This visual method supports the findings from algebraic calculation.