Sec. 6-5: Parallel & Perpendicular Lines. 1. Parallel Lines: // Lines that never intersect. Slopes are the same. 2. Perpendicular Lines: ┴ Lines that.

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Sec. 6-5: Parallel & Perpendicular Lines

1. Parallel Lines: // Lines that never intersect. Slopes are the same. 2. Perpendicular Lines: ┴ Lines that intersect at 90° angles. Slopes are OPPOSITE RECIPROCALS. Identify the following lines as // or ┴ or neither.

y = 3x – 2 y = 3x -12 // because both slopes are 3 2y = -x + 5 y = 2x + 4 ┴ because the 1 st slope is -1/2 & the 2 nd is 2 3x – 2y = -8 x + y = 1 Neither because the 1 st slope is 3/2 & the 2 nd is -1

Writing equations of // & ┴ lines 1.Determine the desired slope. You may have to manipulate the original equation around to pick off the slope. 2.Use the Point-Slope Form y – y = m(x - x) to write the equation, plugging in the desired slope & the given point. 3.Put the equation in the desired format.

Write an equation of a line ┴ 2x – 3y =7 and that goes through the point (-5, 9). 1. First, determine the current line’s slope: (solve for y) 2x – 3y = 7 -2x = -2x -3y = -2x + 7 y = 2/3x - 7/3 so m = 2/3 We need a ┴ slope so m ┴ = -3/2

2.Use y – y = m(x – x) and plug in the new slope and the given point. m = -3/2 and use the point (-5, 9) y – y = m(x – x) y – 9 = -3/2(x + 5) Y – 9 = -3/2x - 15/2 +9 = +9 y = -3/2 x - 15/2 + 18/2 y = -3/2x + 3/2

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