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3-6:Slope of Parallel and Perpendicular Lines

3-6:Slope of Parallel and Perpendicular Lines. Objective : To relate slope of parallel and perpendicular lines, and to write equations of parallel and perpendicular lines. . (http://www.regentsprep.org/Regents/math/ALGEBRA/AC3/Lparallel.htm). Slopes of Parallel Lines.

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3-6:Slope of Parallel and Perpendicular Lines

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  1. 3-6:Slope of Parallel and Perpendicular Lines Objective: To relate slope of parallel and perpendicular lines, and to write equations of parallel and perpendicular lines.

  2. (http://www.regentsprep.org/Regents/math/ALGEBRA/AC3/Lparallel.htm)(http://www.regentsprep.org/Regents/math/ALGEBRA/AC3/Lparallel.htm)

  3. Slopes of Parallel Lines • Slopes of parallel lines are equal • Any 2 vertical lines are parallel; Any 2 horizontal lines are parallel • Test whether 2 non-vertical or non-horizontal lines are || by comparing slopes EXAMPLE: l1 contains points A(1,5) and B(3,1). l2contains points C(3,3) and D(1, -4) Are the 2 lines parallel? Explain.

  4. Are the two lines parallel? Line 1 contains P(0,3) and Q(-2, 5) Line 2 contains R(0,-7) and S(3,-10)

  5. Are the lines 4y-12x=20 and y=3x-1 parallel? Explain. Compare Slopes by re-writing in slope-intercept form:

  6. Slope and Perpendicular Lines • Perpendicular Lines have slopes that are opposite, reciprocals of each other • Their slopes’ product is -1 • Any vertical and any horizontal line are perp. Slope: Perpendicular Slope:

  7. Are the 2 lines perpendicular? To answer this question, do the following: • Find their slopes • If their slopes are opposite, reciprocal, then they are perpendicular. Example: line 1: (-2,3) and (6, -3) line 2: (-3,-2) and (0,2)

  8. Are the 2 lines perpendicular: 1. 2x-y=5 y= -1/2x +7 • y=5 x=-2 3. -3x+y=5 3x –y =4

  9. Writing Equations of Parallel Lines Write an equation of a line parallel to y=-2x +3 that contains the point (1, -2). Identify slope. Use this slope and given point to write equation:

  10. Writing equations for perpendicular lines. • Identify slope of given line. • Find the slope of the line perpendicular to the given line (opposite, reciprocal) • Use the slope from step 2 and given point to write new equation.

  11. Write the equation for the line perpendicular to y=-3x-5 that contains the point (-3, 7).

  12. What do you see when you see an empty parrot cage? A polygon. HAHAHAHAHAHAHA………………………..

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