# 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 |