The demand curve is a graph used in economics to demonstrate the relationship between the price of a product and the demand for that same product. The graph is calculated using a linear function that is defined as P = a - bQ, where "P" equals the price of the product, "Q" equals the quantity demanded of the product, and "a" is equivalent to non-price factors that affect the demand of the product. Given a table, it is simple to solve for the slope of a demand curve at a point using the linear demand curve equation or the equation for the slope of a linear equation.
Write down a set of values for a certain point on the graph from the data provided within the table. For example, if the table states that at point (30, 2) the value of Q = 30, the value of P = 2 and the value of a = 4, write them out on a piece of paper for easy access.
Insert the values into the linear demand curve equation, Q = a - bP. For example, using the above values found from the example table, insert Q = 30, P = 2 and a = 4 into the equation: 30 = 4 - 2b.
Isolate the b variable on one side of the equation in order to solve for the slope. For example, using algebra we find: 30 = 4 - 2b becomes 30 - 4 = - 2b, becomes -26 = 2b, becomes -26 ÷ 2 = b.
Solve for the slope "b" using your calculator or by hand. For example, solving the equation -26 ÷ 2 = b finds b = -13. So, the slope for this set of parameters equals -13.
Write down the x and y values from two points listed on a demand curve's coordinate table. In the case of a demand curve, the point "x" equals the quantity demanded of a product and the point "y" equals the price of the product at that level of demand.
Insert these values into the slope equation: slope = change in y / change in x. For example, if the table states that the values of of x1 = 3, x2 = 5, y1 = 2 and y2 = 3, the slope equation is set up like this: slope = (3 - 5) ÷ (2 - 3).
Solve the slope equation to find the slope of the demand curve between the two chosen points. For example, if the slope = (3 - 5) ÷ (2 - 3), then slope = -2 ÷ -1 = 2.
