# 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 ).

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