2-3C Parallel and Perpendicular Lines Objectives: How do you know if slopes are parallel or perpendicular? What are skew lines?

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

Example 1 Determine whether these lines are parallel. y = 4x -6 and The slope of both lines is 4. So, the lines are parallel.

Example 2 Determine whether these lines are parallel. y – 2 = 5x + 4 and -15x + 3y = 9 +2 +2 +15x +15x y = 5x + 6 3y = 9 + 15x 3 3 y = 3 + 5x y = 5x + 3 The lines have the same slope. So they are parallel.

Example 3 Determine whether these lines are parallel. y = -4x + 2 and +2y + 2y 2y - 5 = 8x +5 +5 2y = 8x + 5 2 2 Since these lines have different slopes, they are not parallel.

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

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

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

Skew lines Skew lines are noncoplanar lines. (Noncoplanar lines cannot intersect.)

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.

2-3C Parallel and Perpendicular Lines Objectives: To determine whether the graphs of two equations are perpendicular

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.

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.

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.

Practice Determine whether these lines are perpendicular. 1) 2y – x = 2 and y = -2x + 4 1. no 2) 4y = 3x + 12 and -3x + 4y – 2 = 0 2. no

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

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

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