10.6 Parallel and Perpendicular Lines CORD Math Mrs. Spitz Spring 2007.

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Presentation transcript:

10.6 Parallel and Perpendicular Lines CORD Math Mrs. Spitz Spring 2007

Objectives: Write an equation of a line that passes through a given point and is parallel or perpendicular to the graph of a given equation.

Assignment pp #5-29 all

Definition What is the slope of a line y = 10 x? What is the slope of a line y = 10x + 5? If two lines have the same slope, then they are parallel All vertical lines are parallel.

Other facts A quadrilateral four-sided figure. A parallelogram is a quadrilateral with two sets of parallel sides.

Ex. 1: Determine if the quadrilateral shown at the right is a parallelogram. Since parallel lines have the same slope, find and compare the slope of the lines containing each side. Use: The lines containing the opposite sides of the quadrilateral are parallel, so the quadrilateral is a parallelogram.

Ex. 2: Find an equation of the line that passes through (4, -2) and is parallel to the graph of 5x – 2y = 6. Use slope-intercept form. The slope of the graph of 5x – 2y = 6 is: Therefore, the slope of a parallel line is 5/2. Why? Parallel lines have the same slope.

Ex. 2: Find an equation of the line that passes through (4, -2) and is parallel to the graph of 5x – 2y = 6. Use slope-intercept form. Next, substitute (4, -2) into the equation above and solve for b.

Line l is shown in the figure below at left. Suppose line l is rotated counterclockwise 90° to form line l1. After the rotation, line l1 is perpendicular to line l.