Question

Find if the lines are parallel, perpendicular, or neither -x+2y=6 & y= -1/2x-7

Answer 1

The answer is neither

Explanation:

Rearranging the equations making y is the subject of the equation and also keeping the coefficient of y '+1' :

1.
`- x + 2y = 6`

`2y = x + 6`

`(2)/(2)y = (1)/(2)(x + 6)`

`y = (1)/(2)x + (6)/(2)`

`y = (1)/(2)x + 3` ---- (equation i)

2.
`y = -(1)/(2)x -7`--- (equation ii)

Focus on the slopes of the two lines.

1. If the two slopes are exactly the same, the lines are parallel

2. If the two slopes are negative reciprocal of each other, the lines are perpendicular

The two slopes are
`(1)/(2)` and
`-(1)/(2)`. They are neither the same nor negative reciprocal to each other.

∴ The answer is neither