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2.5 Writing Equation of a Line Part 2 September 21, 2012 Slopes of Parallel Lines In a coordinate plane, 2 lines are parallel if and only if they have the same slope. Write Equations of Parallel Lines Write an equation of the line that passes through( – 1, 4) and is parallel to the line y = – 2x + 5 . The given line has a slope of –2. Any line parallel to this line will also have a slope of –2. y = mx + b 4 =-2(-1) + b 4 = 2+ b -2 -2 2=b y = -2x + 2 Substitute 4 for y, -1 for x and -2 for m Simplify Solve for b Another Example Find the equation of a line going through the point (3, -5) and parallel to 2 y x 8 3 Using the point-slope equation where the slope m = -2/3 and the point is (3, -5) we get 2 y (5) ( x 3) 3 2 5 (3)b 2 3 y5 x2 OR 3 5 2 b 2 y x 3 3 3 b 2 y x3 3 Checkpoint Find the equation of the line going through the point (4,1) and parallel to y 3x 7 (click mouse for answer) y 1 3 x 4 y 1 3 x 12 y 3 x 13 1 3(4) b 1 12 b 13 b y 3 x 13 Find the equation of the line going through the point (-2,7) and parallel to 2 x y 8 (click mouse for answer) y 7 2 x 2 7 2(2) b y 7 2 x 2 y 7 2 x 4 y 2 x 3 7 4b 3b y 2 x 3 Slopes of Perpendicular Lines In a coordinate plane, 2 lines are perpendicular if and only if their slopes are opposite reciprocal of each other (or their product is –1) Equation of a line Perpendicular to another line Find the equation of a line going through the point (3, -5) and perpendicular to 2 y x8 3 The slope of the perpendicular line will be m = 3/2. Using the point-slope equation where the slope m = 3/2 and the point (3, -5) we get 3 y (5) ( x 3) 2 3 9 y5 x 2 2 3 19 y x 2 2 3 5 (3) b 2 9 5 b 2 19 b 2 3 19 y x 2 2 Checkpoint Find the equation of the line going through the point (-6, -5) and perpendicular to y = -x + 2. y = x +1 Find the equation of the line going through the point (-2,7) and perpendicular to 2 x y 8 y 7 1 x 2 2 y7 1 2 x 2 y 7 1 x 1 2 y 1 x8 2 Homework: 2.5 p.98 #37-42ALL, 44-50even