# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

Compute properties of the secant line to a curve between two points

Contributed by:
Wolfram|Alpha Math Team

ResourceFunction["SecantLine"][ returns an association of properties of the secant line to | |

ResourceFunction["SecantLine"][ returns the value of the secant line property | |

ResourceFunction["SecantLine"][ returns information relating to one, among possibly several, of the secant lines to | |

ResourceFunction["SecantLine"][ returns information relating to one, among possibly several, of the secant lines to |

Allowed values of *prop* are:

"SlopeInterceptEquation" | equation of the secant line in slope-intercept form |

"StandardFormEquation" | equation of the secant line in standard form |

"PointSlopeEquation" | equation of the secant line in point-slope form |

"Slope" | slope of the secant line |

"HorizontalIntercept" | horizontal intercept for the secant line equation |

"VerticalIntercept" | vertical intercept for the secant line equation |

"Plot" | plot of the secant line equation |

All | Association of information returning all allowed properties |

If *expr* does not have head Equal, then *expr* is treated as an expression defining *y* in terms of *x*. In other words, ResourceFunction["SecantLine"][*expr*,{*x*,*a*},*y*,…] is equivalent to ResourceFunction["SecantLine"][*y*==*expr*,{*x*,*a*},*y*,…] if *expr* has a head other than Equal.

If only one coordinate of the intersection points are given, the other coordinates are inferred. For expressions that are multivalued at the given value of *x* or *y*, information on only one of potentially several secant lines is returned.

Compute the slope-intercept equation of the secant line to a curve between two points:

In[1]:= |

Out[1]= |

Visualize this result:

In[2]:= |

Out[2]= |

Compute the slope of this secant line:

In[3]:= |

Out[3]= |

Compute the horizontal intercept of this secant line:

In[4]:= |

Out[4]= |

Get the standard-form equation of this secant line:

In[5]:= |

Out[5]= |

Get an Association of properties of a secant line to a curve:

In[6]:= |

Out[6]= |

Get just the point-slope equation of this secant line:

In[7]:= |

Out[7]= |

The first argument to SecantLine can be an implicit definition of a curve:

In[8]:= |

Out[8]= |

If a secant line is parallel to a coordinate axis, its intercept with that axis is None:

In[9]:= |

Out[9]= |

Requesting secant line information about a point that is not on the curve will result in an error message:

In[10]:= |

Out[10]= |

If one coordinate is not specified, information on only one of the possible secant lines at the given coordinate values is returned:

In[11]:= |

Out[11]= |

The slope of a vertical secant line cannot be computed:

In[12]:= |

Out[12]= |

Use SecantLine and the resource function TangentLine within Manipulate to create an interactive tool that demonstrates the relationship between the tangent line to a curve at a point *x*=-1 and the secant line between *x*=-1 and another point that approaches *x*=-1:

In[13]:= |

Out[14]= |

This work is licensed under a Creative Commons Attribution 4.0 International License