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2-3C Parallel and Perpendicular Lines

Objectives: How do you know if slopes are parallel or perpendicular? What are skew lines?

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Parallel Lines Parallel lines are lines in the same plane that never intersect. Parallel lines have the same slope. -8 -6 -4 -2 2 4 6 8

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Example 1 Determine whether these lines are parallel. y = 4x -6 and

The slope of both lines is 4. So, the lines are parallel.

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Example 2 Determine whether these lines are parallel. y – 2 = 5x + 4

and -15x + 3y = 9 +15x x y = 5x + 6 3y = x y = 3 + 5x y = 5x + 3 The lines have the same slope. So they are parallel.

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Example 3 Determine whether these lines are parallel. y = -4x + 2 and

+2y y 2y – 5 = 8x 2y = 8x + 5 Since these lines have different slopes, they are not parallel.

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Practice Determine whether the graphs are parallel lines. 1. no

1) y = -5x – 8 and y = 5x + 2 2) 3x – y = -5 and 5y – 15x = 10 2. yes 3. no 3) 4y = -12x + 16 and y = 3x + 4

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Practice Write the slope-intercept form of the equation of the line passing through the point (0,2) and parallel to the line 3y – x = 0. 3y = x Y = ⅓x m = ⅓ y = ⅓x + b 2 = ⅓(0) + b 2 = b y = ⅓x + 2

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Practice Determine whether the graphs of the equations are parallel lines. 3x – 4 = y and y – 3x = 8 1. yes 2) y = -4x + 2 and -5 = -2y + 8x 2. no

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Skew lines Skew lines are noncoplanar lines.

(Noncoplanar lines cannot intersect.)

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Name all the lines parallel to that contain edges of the cube.

Name all of the lines that are skew to that contain edges of the cube.

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2-3C Parallel and Perpendicular Lines

Objectives: To determine whether the graphs of two equations are perpendicular

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Perpendicular Lines Perpendicular lines are lines that intersect to form a 900 angle. -8 -6 -4 -2 2 4 6 8 The product of the slopes of perpendicular lines is -1.

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Example 1 Determine whether these lines are perpendicular. and

y = -3x – 2 m = -3 Since the product of the slopes is -1, the lines are perpendicular.

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Example 2 Determine whether these lines are perpendicular. y = 5x + 7

and y = -5x – 2 m = 5 m = -5 5 x (-5) = -25 Since the product of the slopes is not -1, the lines are not perpendicular.

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Practice Determine whether these lines are perpendicular.

1) 2y – x = 2 and y = -2x + 4 1. no 2) 4y = 3x and -3x + 4y – 2 = 0 2. no

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Example 3 Write an equation for the line containing (-3,-5) and perpendicular to the line y = 2x + 1. First, we need the slope of the line y = 2x + 1. m = 2 Second, we need to find out the slope of the line that is perpendicular to y = 2x + 1. Lastly, we use the slope formula to find our equation. y = mx + b y = 2x + b −5 = 2(−3) +b −5 = −6 +b b = 1 y = 2x + 1

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Practice Write an equation for the line containing the given point and perpendicular to the given line. 1) (0,0); y = 2x + 4 y = −½x 2) (-1,-3); x + 2y = 8 Y = −2x +1

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Homework p. 144, 1-9, 15-17

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