Question

Please help with these questions thank youu!!​

Answer 1

#1

`\\ \rm\Rrightarrow 2y=x-4`

`\\ \rm\Rrightarrow y=x/2-2`

• m=1/2

Parallel lines have equal slope

Equation in point slope form

`\\ \rm\Rrightarrow y-4=1/2(x-1)`

`\\ \rm\Rrightarrow 2y-8=x-1`

`\\ \rm\Rrightarrow x-2y+7=0`

#2

`\\ \rm\Rrightarrow 1/2y-3x=2`

`\\ \rm\Rrightarrow 1/2y=3x+2`

`\\ \rm\Rrightarrow y=6x+4`

• m=6

Parallel lines have equal slope

Equation of line

`\\ \rm\Rrightarrow y-6=6(x+2)`

`\\ \rm\Rrightarrow y-6=6x+12`

`\\ \rm\Rrightarrow 6x-y+18=0`

#3

`\\ \rm\Rrightarrow 1/k x+5=3y\implies y=x/3k+5/3`

• m1=1/3k

`\\ \rm\Rrightarrow y=(2/k+3)x-6/(k+3)`

• m2=2/k+3

Slopes remain same

`\\ \rm\Rrightarrow (1)/(3k)=(2)/(k+3)`

`\\ \rm\Rrightarrow k+3=6k`

`\\ \rm\Rrightarrow 5k=3`

`\\ \rm\Rrightarrow k=3/5`