Question

Determine whether each pair of lined is perpendicular parallel or neither

Answer 1

given a pair of lines

a parallel pair of lines is given whe the slope of both lines is the same or

`m1=m2`

perpendicular is given when slope1 multiply by slope2 equals -1 or

`m1*m2=-1`

first pair.

`2x-4y=-4`

solving for y

`y=(4+2x)/(4)=(x+2)/(2)`
`y=(1)/(2)x+1`

then m1=1/2

`3x-6y=9`

solving for y

`-6y=9-3x`
`y=(x-3)/(2)`
`y=(1)/(2)x-(3)/(2)`

then m2=1/2

since both slopes are equal, first pair has paralel lines

2nd pair

`2x+3y=12`
`y=(12-2x)/(3)`
`y=-(2)/(3)x+4`

then m1= -2/3

`5x-4y=7`
`y=(-7+5x)/(4)`
`y=(5)/(4)x-(7)/(4)`

m2 = 5/4

since

`m1*m2=-1`
`-(2)/(3)*(5)/(4)=(10)/(12)`

second pair is neither parallel nor perpendicular

3rd pair

`x+(1)/(2)y=2`
`y=2(2-x)`
`y=-2x+4`

then m1 = -2

`(1)/(2)x+2y=4`
`2y=4-(1)/(2)x`
`y=-(1)/(4)x+2`

then m2=-1/4

`m1*m2=-2*-(1)/(4)=2`

3rd pair is not a paralel line nor perpendicular line