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 – 2y = 3x -12 // because both slopes are 3

2y = -x + 5y = 2x + 4┴ because the 1st slope is -1/2 & the 2nd is 2

3x – 2y = -8x + y = 1Neither because the 1st slope is 3/2 & the 2nd 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 = +9y = -3/2 x - 15/2 + 18/2

y = -3/2x + 3/2