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Writing Parallel and Perpendicular Lines Part 1 Parallel Lines // (symbol) All parallel lines have the same slope. Parallel lines will NEVER CROSS. Since Parallel lines don’t cross, we say they have NO solution. The slope of all vertical lines is undefined. (No Slope) The slope of all horizontal lines is zero. Given slope: Parallel slope: 2 A) y = x 7 3 2 m 3 B) y = 4x 8 m4 C ) y = 5x 3 m 5 7 D) y = x4 15 7 m 15 1) Find line parallel to y = 6x 4 and goes through (-6, 4) ( x1 , y1 ) Step 1 Step 2 Step 3 Find m Find b Find equation Plug in x,y, & m Plug in m & b From given eq. y mx b y mx b 4 6(6) b 4 36 b 36 36 6 x 40 y __ __ y 6x 4 m6 now go to next column 40 b y 6 x 40 3 x 8 y 8 2) Find line parallel to through (6, -2) Step 2 Step 1 ( x , y ) Find b 1 1 Find m— Plug in x,y, & m solve for y y mx b From given eq. 3 x 8 y 8 2 3 (6) b 3x 3x (8) (8)8 18 (8) 8 y 3 x 8 8 3 8 8 y 8 x 1 3 m 8 now go to next column 2 8 16 18 18 18 2 8 b 8b 8b 1 4 8 b and goes Step 3 Find equation Plug in m & b y mx b 1 3 4 8 x __ y __ 3 1 y x 8 4 Perpendicular Lines (symbol) Lines that form a 90° Angle. Perpendicular Lines have one solution written as an ordered pair. Perpendicular Lines’ slopes are NOT the same (negative reciprocals). Do 2 things… FLIP the slope & CHANGE the SIGN 3 m 2 2 m 3 Given slope: 5 A) m 6 1 B) m 3 Perpendicular slope: 6 m 5 3 m 3 1 4 C) m 7 7 m 4 D) m 9 1 m 9 3) Find line perpendicular to through (-6, 4) 1 y = x+4 and goes 3 ( x1 , y1 ) Step 1 Step 2 Step 3 1 y x4 3 4 3(6) b 4 18 b 18 18 14 y __3x __ FLIP the slope & CHANGE the SIGN 3 m 3 1 now go to next column 14 b y 3 x 14 4) Find line perpendicular to goes through (4, 7) Step 1 ( x1 , y1 ) 5 x 2 y 10 5x 5x FLIP the slope & CHANGE the SIGN 2 m 5 now go to next column Step 2 5 (5) 7 8 5 35 8 (5) b 5b 8 8 27 5b 5 5 27 5 b and Step 3 y mx b 2 7 (4) b 2 y 5 x 10 (5) 2 2 2 5 y x5 2 2 x 5 y 10 y mx b 27 2 5 5 x __ y __ 2 27 y x 5 5