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'slope'
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| Title of object: |
slope |
| Canonical Name: |
Slope |
| Type: |
Definition |
| Created on: |
2004-11-08 13:50:21 |
| Modified on: |
2007-05-27 15:24:30 |
| Classification: |
msc:51N20 |
| Keywords: |
direction angle |
| Synonyms: |
slope=angle coefficient (?) |
Revision comment (for changes between this and next version):
| added the condition of parallelism |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx} |
Content:
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.
The slope is equal to the \PMlinkname{tangent}{DefinitionsInTrigonometry} of the direction angle of the line.
\begin{center}
\includegraphics{slope}
\end{center}
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. |
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