# How o write an equation which is parallel and perpendicular to the given lines below? (1) y= -5x (2) y= 1/3x-1 (3) 2x-4y=3

May 20, 2018

Parallel lines have the same slope, whereas perpendicular lines have negative reciprocal slopes.

Equation 1: $y = - 5 x$

• Parallel
A parallel line will have the same slope. However, it can be transitioned vertically by a constant value.
$y = - 5 x + c$
• Perpendicular
The perpendicular line will have a negative reciprocal slope. This means we divide $1$ by the slop and change its sign. The constant is also necessary.
$y = \frac{1}{5} x + c$

Equation 2: $y = \frac{1}{3} x - 1$

• Parallel
In this case, the equation already has a constant, but it will be different in the parallel line.
$y = \frac{1}{3} x + c$
• Perpendicular
$y = - 3 x + c$

Equation 3: $2 x - 4 y = 3$

In this case, we must first rearrange the equation to be in the $y = m x + b$ form.

$- 4 y = - 2 x + 3$

$y = \frac{- 2}{-} 4 x + \frac{3}{-} 4$

$y = \frac{1}{2} x - \frac{3}{4}$

• Parallel
$y = \frac{1}{2} x + c$
• Perpendicular
$y = - 2 x + c$