slope

The slope of a 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 y-intercept).

The slope is equal to the tangent (http://planetmath.org/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.

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.

Title	slope
Canonical name	Slope
Date of creation	2013-03-22 14:48:10
Last modified on	2013-03-22 14:48:10
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	14
Author	pahio (2872)
Entry type	Definition
Classification	msc 51N20
Synonym	angle coefficient (?)
Related topic	Derivative
Related topic	ExampleOfRotationMatrix
Related topic	ParallellismInEuclideanPlane
Related topic	SlopeAngle
Related topic	LineInThePlane
Related topic	DifferenceQuotient
Related topic	DerivationOfWaveEquation
Related topic	IsogonalTrajectory
Related topic	TangentOfHyperbola