Question

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

Answer 1

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

Equation 1: `y=-5x`

• Parallel
  A parallel line will have the same slope. However, it can be transitioned vertically by a constant value.
  `y=-5x+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=1/5x+c`

Equation 2: `y=1/3x-1`

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

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

In this case, we must first rearrange the equation to be in the `y=mx+b` form.

`-4y=-2x+3`

`y=(-2)/-4x+3/-4`

`y=1/2x-3/4`

• Parallel
  `y=1/2x+c`
• Perpendicular
  `y=-2x+c`