1. 4.5A Find and Use Slopes of Lines

2. Recall: The slope of a non-vertical line is the ratio of vertical change (rise) to horizontal change (run) between any two points on the line.

5. Up 2 Right 8

6. down 4 Right 6

7. Slopes of Intersecting Lines - The steeper line has the slope with _greater absolute value___. Slopes of Parallel Lines – In a coordinate plane, two non-vertical lines are parallel if and only if __they have the same slope_____________________________ Any two __vertical__ lines are parallel.

8. Slopes of Perpendicular Lines – In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is _-1__ (or their slopes are _negative reciprocals__). Vertical and horizontal lines are perpendicular.

9. K and n are parallel (they have the same slope) J is steepest (it has the greatest absolute value)

10. Example - What is the slope of any line perpendicular to the line through (-2,5) and (3, -1)?

11. Example - Given points A(1,-4), B(- 1,2), C(4,2), and D(5,-1), use slopes to determine whether AC ⊥ DB.

13. Example - Line q passes through the points (1, 2) and (-4, 5). Line t passes through the points (-2, -1) and (10, 7). Which line is steeper, q or t? T is steeper because it’s absolute value is larger.