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Slope

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The slope of a line can be intuitively defined as how steep the line is, relative to some coordinate system. To be more precise, given a line \mathcal L in the Cartesian plane and two points, (x_1,y_1) and (x_2,y_2), on \mathcal L with x_1 \neq x_2, the slope m of \mathcal L is equal to \frac{y_1-y_2}{x_1-x_2}. If all points on \mathcal L have the same x-coordinate (abscissa), we say that \mathcal L has infinite slope.

Other expressions for the slope are

\frac{\rm{rise}}{\rm{run}},
\frac{\Delta y}{\Delta x} (read "delta y over delta x"),
or \frac{\rm{change \ in \ } y}{\rm{change \ in \ } x}.


If \theta is the directed angle between the x-axis and \mathcal L, the slope is also given by m = \tan \theta.


See also

Want to learn how to tackle those tough AMC/AIME/Olympiad counting and probability problems? Check out Art of Problem Solving's Intermediate Counting & Probability by David Patrick.
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