4.5A Find and Use Slopes of Lines. Recall: The slope of a non-vertical line is the ratio of vertical change (rise) to horizontal change (run) between.

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Presentation transcript:

4.5A Find and Use Slopes of Lines

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.

Up 2 Right 8

down 4 Right 6

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.

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.

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

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

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

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.

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