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Warm-Up

Warm-Up. 1.) Using the point slope formula find the equation of a line with slope -2 , passing through the point (1, 3). 2.) Graph the line y = 3x + 4. 3.) Graph the line y = 3x - 2. 4.) What is the slope of the lines in the equations for # 2, 3 above?.

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Warm-Up

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  1. Warm-Up 1.) Using the point slope formula find the equation of a line with slope -2 , passing through the point (1, 3) 2.) Graph the line y = 3x + 4. 3.) Graph the line y = 3x - 2 4.) What is the slope of the lines in the equations for # 2, 3 above?

  2. 4.3 Parallel and Perpendicular Lines Objectives: To determine whether the graphs of two equations are parallel or perpendicular

  3. 8 6 4 2 6 8 -2 -8 -6 -4 2 4 -2 -4 -6 -8 Parallel Lines Parallel lines are lines in the same plane that never intersect. Parallel lines have the same slope.

  4. Example 1 Determine whether these lines are parallel. y = 4x + 2 y = 4x -6 and The slope of both lines is 4. So, the lines are parallel.

  5. Example 2 Determine whether these lines are parallel. -15x + 3y = 9 y – 2 = 5x + 4 and +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.

  6. Example 3 Determine whether these lines are parallel. -5 = -2y + 8x 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.

  7. Example 4 Write the slope-intercept form of the equation of the line passing through the point (1, –6) and parallel to the line y = -5x + 3. slope of new line = -5 y – y1 = m(x – x1) y – (-6) = -5(x – 1) y + 6 = -5x + 5 y = -5x - 1

  8. 8 6 4 2 6 8 -2 -8 -6 -4 2 4 -2 -4 -6 -8 Perpendicular Lines Perpendicular lines are lines that intersect to form a 900 angle. The slopes of perpendicular lines are opposite reciprocals

  9. Example 5 Determine whether these lines are perpendicular. y = -3x - 2 and m = -3 Since the slopes are opposite reciprocals, the lines are perpendicular.

  10. Example 6 Determine whether these lines are perpendicular. y = 5x + 7 y = -5x - 2 and m = -5 Since the slopes are not opposite reciprocals, the lines are not perpendicular.

  11. Example 7 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 point-slope formula to find our equation.

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

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