Geometry: An Interactive Journey to Mastery

Lesson 11: Making Use of Linear Equations

Making Use of Linear Equations

Lesson 11

Topics

x The equation of a line.

x The slopes of parallel and perpendicular lines.

x The perpendicular bisector of a line segment.

x Applications.

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x perpendicular bisector: The perpendicular bisector of a line segment is a line through the midpoint of

the segment and perpendicular to it.

Formulas

x A line of slope mWKURXJKWKHSRLQWͼ௘a, b௘ͽKDVHTXDWLRQyíb = mͼ௘xía௘ͽͼ௘2IFRXUVHWKHUHDUHPDQ\

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x Parallel lines have the same slope.

x If one line has slope m, then a line perpendicular to it has slope m^1 ͼ௘DVVXPLQJWKDWQHLWKHUOLQH

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Summary

The algebraic equation of a line is nothing more than a restatement of our belief that the slope of straight lines is

constant. In this lesson, we develop the equation of a line, discuss the slopes of parallel and perpendicular lines,

and practice our algebraic skills in a variety of geometric settings about lines.