Infinite And Zero Slopes

Many variables are unrelated or independent of one another. For example, the quantity of wristwatches purchased is not related to the price of bananas. In Figure A1- (a) we represent the price of bananas on the vertical axis and the quantity of watches demanded on the horizontal axis. The graph of their relationship is the line parallel to the vertical axis, indicating that the same quantity of watches is purchased no matter what the price of bananas. The slope of such a line is infinite.

Similarly, aggregate consumption is completely unrelated to the nation's divorce rate. In Figure A1- (b) we put consumption on the vertical axis and the divorce rate on the horizontal axis. The line parallel to the horizontal axis represents this lack of relatedness. This line has a slope of zero.

Vertical Intercept

A line can be located on a graph (without plotting points) if we know its slope and its vertical intercept. The vertical intercept of a line is the point where the line meets the vertical axis. In Figure A1-1 the intercept is $50. This intercept means that if current income were zero, consumers would still spend $50. They might do this through borrowing or by selling some of their assets. Similarly, the $50 vertical intercept in Figure A1-2 shows that at a $50 ticket price, IU's basketball team would be playing in an empty arena.

Equation of a Linear Relationship

If we know the vertical intercept and slope, we can describe a line succinctly in equation form. In its general form, the equation of a straight line is y = a + bx where y = dependent variable a = vertical intercept b = slope of line x = independent variable

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