Difference between revisions of "Slope"
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| − | The '''slope''' of a [[line]] can be intuitively defined as how steep the line is. To be more precise, given two points <math>(x_1,y_1)</math> and <math>(x_2,y_2)</math> on | + | 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 <math>\mathcal L</math> in the [[Cartesian plane]] and two points, <math>(x_1,y_1)</math> and <math>(x_2,y_2)</math>, on <math>\mathcal L</math> with <math>x_1 \neq x_2</math>, the slope <math>m</math> of <math>\mathcal L</math> is equal to <math> \frac{y_1-y_2}{x_1-x_2}. </math> If all points on <math>\mathcal L</math> have the same <math>x</math>-coordinate ([[abscissa]]), we say that <math>\mathcal L</math> has [[infinite]] slope. |
| − | + | Other expressions for the slope are | |
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| − | Other | ||
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|or <math>\frac{\rm{change \ in \ } y}{\rm{change \ in \ } x}</math>. | |or <math>\frac{\rm{change \ in \ } y}{\rm{change \ in \ } x}</math>. | ||
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| + | If <math>\theta</math> is the [[directed angle]] between the <math>x</math>-axis and <math>\mathcal L</math>, the slope is also given by <math>m = \tan \theta</math>. | ||
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== See also == | == See also == | ||
* [[Graphing]] | * [[Graphing]] | ||
* [[Algebra]] | * [[Algebra]] | ||
Latest revision as of 20:02, 29 September 2006
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 
in the Cartesian plane and two points, 
and 
, on with 
, the slope 
of is equal to 
If all points on have the same 
-coordinate (abscissa), we say that has infinite slope.
Other expressions for the slope are
|
 (read "delta  over delta "),
|
or  .
|
If 
is the directed angle between the -axis and , the slope is also given by 
.
