# 21 and so the two negatives cancel having a feel for

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the negative of the corresponding terms in Equation M.2.1, and so the two negatives cancel. Having a feel for the meaning of the slope of a line is an extremely important part of developing not only your mathematical but also your economic intuition. The slope is a ratio of changes in 2 variables. If the slope of the graph of an equation is positive , then an increase in one variable is associated with an increase in the other (and similarly, a decrease in one variable is associated with a decrease in the other). If the slope is nega- tive , then an increase in one variable is associated with a decrease in the other (and simi- larly, a decrease in that variable is associated with an increase in the other). If the slope is relatively low in absolute value and the curve is hence relatively ﬂat , then a unit change in the horizontal variable is associated with a relatively small change in the vertical variable. In contrast, if the slope is relatively high in absolute value and the curve is hence relatively steep , then a unit change in the horizontal variable is asso- ciated with a relatively large change in the vertical variable. The two limiting cases occur when the line is horizontal or vertical. If the line is hor- izontal and its slope ∆ y/ x is zero (that is, ∆ y = 0), then no matter how great a change occurs in the horizontal variable, there is no associated change in the vertical variable: it is constant . If in contrast the line is vertical and its slope ∆ y/ x is infinite or undefined (that is, ∆ x = 0), then no matter how great a change occurs in the vertical variable, there is no associated change in the horizontal variable: it is now the one that is constant. The importance of the slope of an equation in an economic model is thus that it encapsulates our assumptions both about the nature of the correlation between two eco- nomic variables (positive or negative) and about the magnitude of the association, or about the degree of responsiveness of changes in one variable to changes in the other. In this context, we can proceed to review the four ways of defining a linear equation. 1. “Standard” (Slope-Intercept) Form : The equation y = 3 + 2 x in Figure M.2-1 has the “standard” form of a linear equation: y = a + b x. (M.2.3) Here a is the vertical intercept , the point at which the graph intersects or cuts the ver- tical axis, with coordinates (0, a ), and b is the slope of the function, ∆ y/ x. Simply looking at the equation, we can visualize the straight line passing through the verti- cal axis 3 units above the origin (since when x = 0 in the equation, y = 3). It slopes

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