MATH 123 Chapter Notes - Chapter 1: Fixed Cost, Marginal Cost

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Linear functions have graphs which are straight lines. The slope of a line is defined as the vertical change (cid:894)the (cid:862)rise(cid:863)(cid:895) over the horizontal change (cid:894)the (cid:862)run(cid:863)(cid:895) as one travels along the line. In symbols, taking two different points (cid:4666)(cid:1876)(cid:2869),(cid:1877)(cid:2869)(cid:4667) and (cid:4666)(cid:1876)(cid:2870),(cid:1877)(cid:2870)(cid:4667) on the line, the slope is: Note that (cid:1876)(cid:2869) (cid:1876)(cid:2870): slope intercept form: (cid:1877)=(cid:1876), point-slope form: (cid:1877) (cid:1877)(cid:2869)=(cid:4666)(cid:1876) (cid:1876)(cid:2869)(cid:4667, vertical line: (cid:1876), horizontal line: (cid:1877)= Two lines are parallel if and only if they have the same slope, or if they are both vertical. Two lines are perpendicular if and only if the product of their slopes is , or if one is vertical and the other horizontal. The slope-intercept and point-slope formulas can be used to find the equation of a line, given a point and the slope or given two points. A relationship is defined by: (cid:1877)=(cid:4666)(cid:1876)(cid:4667)=(cid:1876)+ is a linear function.

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