slopeSlope2004-11-08 13:50:212008-02-16 10:50:05Definitionrelated ratesparallelism of lines\usepackage{amssymb}
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The {\em slope} of a \PMlinkescapetext{straight} line in the $xy$-plane expresses how great is the change of the ordinate $y$ of the point of the line per a unit-change of the abscissa $x$ of the point; it requires that the line is not vertical.
The slope $m$ of the line may be determined by taking the changes of the coordinates between two arbitrary points $(x_1,\,y_1)$ and $(x_2,\,y_2)$ of the line:
$$m = \frac{y_2-y_1}{x_2-x_1}$$
The equation of the line is
$$y = mx+b,$$
where $b$ indicates the intersection point of the line and the $y$-axis (one speaks of {\em y-intercept}).
The slope is equal to the \PMlinkname{tangent}{DefinitionsInTrigonometry} of the slope angle of the line.
Two non-vertical lines of the plane are parallel if and only if their slopes are equal.
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In the previous picture, the blue line given by\, $3x-y+1 = 0$\, has slope $3$, whereas the red one given by\,
$2x+y+2 = 0$\, has slope $-2$.\, Also notice that positive slopes represent ascending graphs and negative slopes represent descending graphs.