In Chapter 1 the relationship between two variables y and x was assumed to be linear and could be written
Here a is the intercept term, or the value of y when x = 0, and b is the slope or gradient, since if x increases by 1, y increases by b. For a linear function the slope is a constant. If the equation represents a cost function, with x as the level of output (where x >0) and y as the total cost, then b is the marginal cost of an extra unit of output. Here it is assumed that output and costs vary continuously so that the equation is valid for all positive values of x. We saw that the graph of such an equation is a straight line.
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© K. Holden and A. W. Pearson 1992