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 (x1,y1) and (x2,y2) of the line:


The equation of the line is


where b indicates the intersectionMathworldPlanetmathPlanetmath point of the line and the y-axis (one speaks of y-interceptMathworldPlanetmath).

The slope is equal to the tangent ( of the slope angle of the line.

Two non-vertical lines of the plane are parallelMathworldPlanetmathPlanetmath 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