Find the slope

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To write the equation of a line parallel to a given line through a given point:

  1. Find the slope of the given line.
  2. Use that slope and the point on the new line to write the equation of the new line. 

    y − y1= m(x − x1)

To write the equation of a line perpendicular to a given line through a given point:

  1. Find the slope of the given line.
  2. Use the opposite reciprocal of that slope and the point on the new line to write the equation of the new line. 

    y − y1= m(x − x1)

To write the equation of a horizontal or vertical line through a given point:

Line TypeSlope of the LIneEquation Form
HorizontalZero
m = 0		y = number
VerticalUndefinedx = number

Relationships of horizontal and vertical lines to other horizontal and vertical lines:

Line TypeRelationship to Horizontal LinesRelationship to Vertical Lines
HorizontalParallelPerpendicular
VerticalPerpendicularParallel

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