1. Section 6.6 Parallel and Perpendicular Lines

2. Definitions Lines that lie in the same plane and never intersect are called parallel lines. All vertical lines are parallel. If two non-vertical lines are parallel, then they have equivalent slopes.

3. Definitions Lines that intersect at right angles are called perpendicular lines. All vertical and horizontal lines are perpendicular to one another. If two lines are perpendicular to one another, then the slopes should be negative reciprocals of one another. If two lines are perpendicular to one another, then the product of the two slopes should equal -1.

4. If we are given a line, how do we construct a line parallel or perpendicular to that line?

5. Questions to ask yourself: What information do we need to construct a line? What information do we need to construct a parallel line? What information do we need to construct a perpendicular line?

6. Example 1: Constructing Parallel Lines Write an equation in slope-intercept form of the line that passes through (4,0) and is parallel to the graph of 4x-3y=2.

7. Your turn! Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of each equation:  (9,3), 5x-6y=2  (0,4), 2y=5x-7  (7,-2), x-y=0

8. Example 2: Constructing Perpendicular Lines Write the slope-intercept form of an equation that passes through (8,-2) and is perpendicular to the graph of 5x-3y=7.

9. Your turn! Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of each equation:  (8,5), 7x+4y=23  (0,0), 9y=3-5x  (-2,7), 2x-5y=3