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Parallel and Perpendicular Lines Chapter 3, Section 5 Video https://www.youtube.com/watch?v=Rew54K6mYUo Lesson and Notes Slope of Parallel and Perpendicular Lines Practice Review: Write the equation of a line from a graph. -2 +4 +4 =-2 -2 Parallel lines Lines in the same plane that do not intersect are called parallel lines. Parallel lines have the same slope. 10 1 2 3 4 5 6 7 8 9 – 10 1 2 3 4 5 6 7 8 9 1– 10 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 Notes: Write the equation of a parallel line y 10 9 8 7 6 5 4 3 2 1 – 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 –1 –2 –3 –4 –5 –6 –7 –8 –9 – 10 1 2 3 4 5 6 7 8 9 10 x Practice. Write the equation of a parallel line. Write the equation of a line parallel to the line shown below and passing through point (1, 2) (1, 2) M=2/3 and b is -1 so -2 Y-intercept Step 2: Substitute into y = mx + b 2 1 (1 ) b -3 1 b M =-2 = 2 -3 3 The slope is 2/3, the y-intercept is 1, so the equation of the parallel line is y=2/3x+1 Practice: Write the equation of a parallel line. 10 1 2 3 4 5 6 7 8 9 – 10 1 2 3 4 5 6 7 8 9 1– 10 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 y Substitute point (1,5) and the slope (3) into y=mx+b 5 3 (1 ) b 10 M= 3 1 9 8 7 +1 6 5 +3 4 3 Y-intercept 2 1 +1 – 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 –1 5 3b 1 2 3 4 5 6 7 8 –2 –3 +3 –4 –5 2b –6 –7 –8 –9 – 10 Y-intercept 9 10 x Perpendicular Lines Opposite reciprocals???? Lines that intersect at right angles are called perpendicular lines. The slopes of these lines are opposite reciprocals. 3….. 1 3 1 4 ... 4 10 1 2 3 4 5 6 7 8 9 – 10 1 2 3 4 5 6 7 8 9 1– 10 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 Write the equation of a perpendicular line. Graph the lines. y 10 9 8 7 6 5 Y-intercept -2 4 3 2 1 – 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 –1 1 +1 –2 –3 –4 –5 –6 –7 –8 –9 – 10 2 3 4 5 6 7 8 9 10 y 10 9 Flip the slope over and change the sign to the opposite. If the original slope is positive, the new one will be negative. If the original is negative, the new one will be positive. (y=7/3)x+10 8 7 6 5 4 3 2 1 – 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 –1 –2 –3 –4 7 3 3 –5 –6 –7 7 –8 –9 – 10 1 2 3 4 5 6 7 8 9 10 x 1– 10 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 3 y 10 9 7 Plug the new slope and the point (-1, 1) into y = mx +b (y=7/3)x+10 8 7 6 5 4 -7 3 y 3 7 x 4 2 1 – 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 –1 7 –2 –3 –4 –5 –6 –7 –8 –9 – 10 1 2 3 4 5 6 8 9 +3 7 10 x 10 Group Activity (click for answers) 9 8 7 6 5 4 3 2 1 – 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 –1 –2 –3 –4 –5 –6 –7 –8 –9 – 10 1 2 3 4 5 6 7 8 9 10 x 10 1 2 3 4 5 6 7 8 9 – 10 1 2 3 4 5 6 7 8 9 1– 10 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 Practice: Writing Equation of a Perpendicular Line y 10 9 8 7 6 5 4 -3 3 +1 2 1 – 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 –1 –2 –3 –4 –5 –6 –7 –8 –9 – 10 1 2 3 4 5 6 7 8 9 10 x Practice: Writing Equation of a Perpendicular Line y 10 9 8 7 6 5 4 3 2 1 – 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 –1 –2 –3 –4 –5 –6 –7 –8 –9 – 10 1 2 3 4 5 6 7 8 9 10 x Notes: Solutions Quiz http://www.classzone.com/etest/viewTestPractice.htm?te stId=4498 http://www.classzone.com/etest/viewTestPractice.htm?testI d=4499