Lesson Info Prototype Math Lesson Related Standards CCProve the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Vocabulary---- Prerequisite Vocabulary: parallel, perpendicular, slope-intercept, point-slope, reciprocal Prototype Math Lesson
space for on-screen teacher When two lines are either parallel or perpendicular, how are their equations related? Equations of Parallel and Perpendicular Lines
Why do parallel lines have equal slopes? Slope =. This ratio has the same value for any 2 points on either line. Slope measures steepness. Parallel lines have the same steepness no matter where they are positioned. x y l q 2 –1 4 –2
How to Write the Equation of a Line Parallel to a Given Line The line passing through (–2, 1) and (3, –2) is parallel to another line passing through (5, –2). Find the equation of both lines. x y
space for on-screen teacher When two lines are either parallel or perpendicular, how are their equations related? Equations of Parallel and Perpendicular Lines
Why do perpendicular lines have negative reciprocal slopes? The slopes of perpendicular lines have opposite signs. One line rises with + slope. The other line falls with – slope. The slopes are also reciprocals. The rise and the run switch, so changes to its reciprocal. x y
space for on-screen teacher Equations of Parallel and Perpendicular Lines When two lines are either parallel or perpendicular, how are their equations related?
Key Concepts Parallel lines have equal slopes. Perpendicular lines have negative reciprocal slopes. x y l q x y Don’t forget to take the reciprocal and change the sign (+ or –). !
Common Problem Types To check whether two lines are parallel or perpendicular: 1)Find each line’s slope. (You may need to rewrite the equation in y = mx + b form first.) 2)Check whether the slopes are equal or negative reciprocals. To write the equation of a line parallel or perpendicular to a given line: 1)Find the slope of the given line. 2)Find the slope of the new line: Parallel lines.Use the same slope. Perpendicular lines.Use the slope’s negative reciprocal. 3)Write the equation; point-slope form is usually fastest: y – b = m ( x – a )
As a result of this lesson, you now should be able to: Use slope to identify lines that are parallel or perpendicular Write the equation of a line that is parallel or perpendicular to a given line and which passes through a given point Solve a variety of problems using equations of parallel and perpendicular lines