3.4 Find and Use Slopes of Lines

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Presentation transcript:

3.4 Find and Use Slopes of Lines

y x (x1 , y1) (x2 , y2)

Find the slope of the line that passes through (0,6) and (5,2) y Find the slope of the line that passes through (0,6) and (5,2) (x2 , y2) (x1 , y1) x

Postulate Slopes of Parallel Lines In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. Any two horizontal lines are parallel.

Postulate Slopes of Perpendicular Lines In a coordinate plane, two nonvertical lines are perpendicular () if and only if the product of their slopes is –1. Vertical and horizontal lines are perpendicular. Slopes of  lines are opposite reciprocals; one is positive and the other negative.

Determining if lines are perpendicular: Find the slope of both lines. Multiply the slopes. If the product is negative one (-1) the lines are perpendicular.

(0,3) (6,-1) (-4,-3) r b

The slopes of two lines are given The slopes of two lines are given. Thumbs up on your chest if the two lines ARE perpendicular.

The slopes of two lines are given The slopes of two lines are given. Thumbs up on your chest if the two lines ARE perpendicular.

The slopes of two lines are given The slopes of two lines are given. Thumbs up on your chest if the two lines ARE perpendicular.

Decide whether the lines with the given equations are: Perpendicular Parallel Neither

Decide whether the lines with the given equations are: Perpendicular Parallel Neither

Decide whether the lines with the given equations are: Perpendicular Parallel Neither

Write an equation of the line through point (2,3) with a slope of 5. y = mx + b 3 = 5(2) + b -7 = b y = 5x - 7

y = 5x - 7 y = mx + b 6 = 5(5) + b -19 = b y = 5x - 19 Write an equation for a line parallel to this line and passing through point (5,6) y = mx + b 6 = 5(5) + b -19 = b y = 5x - 19

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