1.5 Writing Equations of Parallel and Perpendicular Lines

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Presentation transcript:

1.5 Writing Equations of Parallel and Perpendicular Lines Objective: Write equations of parallel and perpendicular lines

Perpendicular and Parallel Lines

Parallel lines: Two non-vertical lines in a plane are parallel if and only if their slopes are equal and they have no points in common. Two vertical lines are always parallel. The graphs of two equations that represent the same line. Coincide:

Ex.1) Determine whether the graphs of each pair of equations are parallel, coinciding, or neither. a.) 2x + 4y = 4 x + 2y = 5 b.) 5x – 3y = 12 10x – 6y = 24

Perpendicular Lines: Ex. 2) Two non-vertical lines in a plane are perpendicular iff their slopes are opposite reciprocals. A horizontal and a vertical line are always Ex. 2) a.) Write the standard form of the equation of the line that passes through the point (-2,10) and is parallel to the graph of 2x + 5y + 4 = 0 b.) Write the standard form of the equation of the line that passes through the point (2,-3) and is perpendicular to the graph of 6x – 8y -5 = 0

Ex. 3) Determine the equation of the perpendicular bisector of the line segment with endpoints (2,3) and (6,-1).

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