Question

Are the lines with the given equations below parallel, perpendicular, or neither? (1) `y= -5x-2, y= 5x+2` (2) `y= 1/3x-1, y= -3x+2` (3) `2x-4y=3, 4x-8y=7`

Answer 1

1. Neither
2. Perpendicular
3. Parallel

Explanation:

For two lines to be parallel: `m_1=m_2`
For two lines to be perpendicular: `m_1m_2=-1`

1. `-5!=5`, `-5*5=-25!=1`, neither parallel or perpendicular

2. `1/3*-3=-1` perpendicular

3. `2x-4y=3` becomes `y=3/4-(2x)/4=-x/2-3/4`
   `4x-8y=7` becomes `y=-7/8-(4x)/8=-7/8-x/2`

`-1/2=-1/2` parallel