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Understanding Tangent Lines A nonlinear relationship is a relationship between two variables that changes over the range of the variables' values. The slope of a nonlinear function changes at every point on it, reflecting the changing relationship between the variables. A tangent line is a straight line that touches a nonlinear curve at any point. If a relationship between two variables is not linear, the slope changes at different points on the curve. These variables are said to have a nonlinear relationship. To calculate the slope exactly at a single point, you will have to use calculus to take the limit. If you use the "rise over run" calculation between two points, as with a linear relationship, the slope will change at every point. For example, on the left, between output levels of four TVs and sixteen TVs, the slope is six. Note that if you choose different points nearer the bottom of this total product curve, the slope becomes flatter. Between output levels of four TVs and nine TVs, the slope is five. You must use calculus to find the slope of a curvilinear line at any point. At the point you are interested in, the slope of the curve equals the slope of a tangent line at that point. On the left, if you use calculus and find the slope of the tangent line at the output level of four TVs, the slope is four. The important point is that the slope of a nonlinear function changes over the curve.