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STEREOTYPES ABOUT PARALLEL AND PERPENDICULAR LINES They are boring! They have no use in life. PARALLEL AND PERPENDICULAR LINES ARE EVERYWHERE REVIEW: SLOPE INTERCEPT FORM y = mx + b m is the slope of the line b is the y-intercept Life is easy when you’re in slope intercept form Y -INTERCEPT y = mx + b The y-intercept is the y value when x = 0. Visually, the y-intercept is y value when the line crosses the y axis http://www.mathsisfun.com/data/functiongrapher.php (2 , 2 ) SLOPE y = mx + b Slope Slider ∆ ∆ (1 , 1 ) Slope of vertical lines? − − m − − IDENTIFYING THE SLOPE AND THE Y-INTERCEPT 3y = 6x + 9 5y = 10x y = -1 x=3 REVIEW: FINDING THE EQUATION OF THE LINE GIVEN A SLOPE AND A POINT ON THE LINE y = mx + b Given the slope, m, and a point, (x , y), then we can find b, the y-intercept. b = y – mx Once we find b, we can find the equation of the line. PRACTICE: FINDING THE EQUATION OF THE LINE GIVEN THE SLOPE AND A POINT ON THE LINE p = (-2 , 2) m = 4 p = (-3 , 4) m = -2 p = (-2 , 2/3) m = -4/3 GRAPHING ACTIVITY 1. Graph line segments. Be sure that each endpoint is an integer coordinate, such as (1,3) or (-3,0) Compute and record their slope. 2. Then graph a parallel line to each of the three line segments. Compute and record the slopes of the parallel lines. Then delete the parallel lines. 3. Then graph a perpendicular line to each of the three line segments. Compute and record the slopes of the perpendicular lines. PARALLEL LINES Two lines are parallel Slopes are equal The lines never intersec t FIND THE SLOPE OF A PARALLEL LINE y = (1/3)x + 2 y – 1 = 6x 2y = 5x + 3 4y = 8x y=6 x = -3 PERPENDICULAR LINES Two lines are perpendicular Slopes are negative reciprocals The lines intersect at right angle FIND THE SLOPE OF A PERPENDICULAR LINE y = -3x – 2 y = (1/3)x + 2 y – 1 = 6x 2y = 5x + 3 y=6 x = -3 FIND THE EQUATION OF THE PARALLEL LINE THAT PASSES THROUGH THE GIVEN POINT. y = (1/3)x + 2 , p = (2 , -3) 2y = 5x + 3 , p = (1/2 , 2/3) y = 6 , p = (6 , 0) x = -3 , p = (1 , 2) FIND THE EQUATION OF THE PERPENDICULAR LINE THAT PASSES THROUGH THE GIVEN POINT. y = -3x – 2 , p = (-1 , 4) 4y = 8x , p = (1 , 1/3) y = 6 , p = (6 , 0) x = -3 , p = (1 , 2)