| Version 7 |
Version 6 |
| 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 {\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. |
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| 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: |
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: |
| $$m = \frac{y_2-y_1}{x_2-x_1}$$ |
$$m = \frac{y_2-y_1}{x_2-x_1}$$ |
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| The equation of the line is |
The equation of the line is |
| $$y = mx+b,$$ |
$$y = mx+b,$$ |
| where $b$ indicates the intersection point of the line and the $y$-axis. |
where $b$ indicates the intersection point of the line and the $y$-axis. |
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| The slope is equal to the \PMlinkname{tangent}{DefinitionsInTrigonometry} of the direction angle of the line. |
The slope is equal to the \PMlinkname{tangent}{DefinitionsInTrigonometry} of the direction angle of the line. |
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| Two non-vertical lines of the plane are parallel if and only if their slopes are equal. |
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| \begin{center} |
\begin{center} |
| \includegraphics{slope} |
\includegraphics{slope} |
| \end{center} |
\end{center} |
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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\, |
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. |
$2x+y+2 = 0$\, has slope $-2$.\, Also notice that positive slopes represent ascending graphs and negative slopes represent descending graphs. |
