#1
[tex]\\ \rm\Rrightarrow 2y=x-4[/tex]
[tex]\\ \rm\Rrightarrow y=x/2-2[/tex]
Parallel lines have equal slope
Equation in point slope form
[tex]\\ \rm\Rrightarrow y-4=1/2(x-1)[/tex]
[tex]\\ \rm\Rrightarrow 2y-8=x-1[/tex]
[tex]\\ \rm\Rrightarrow x-2y+7=0[/tex]
#2
[tex]\\ \rm\Rrightarrow 1/2y-3x=2[/tex]
[tex]\\ \rm\Rrightarrow 1/2y=3x+2[/tex]
[tex]\\ \rm\Rrightarrow y=6x+4[/tex]
Parallel lines have equal slope
Equation of line
[tex]\\ \rm\Rrightarrow y-6=6(x+2)[/tex]
[tex]\\ \rm\Rrightarrow y-6=6x+12[/tex]
[tex]\\ \rm\Rrightarrow 6x-y+18=0[/tex]
#3
[tex]\\ \rm\Rrightarrow 1/k x+5=3y\implies y=x/3k+5/3[/tex]
[tex]\\ \rm\Rrightarrow y=(2/k+3)x-6/(k+3)[/tex]
Slopes remain same
[tex]\\ \rm\Rrightarrow \dfrac{1}{3k}=\dfrac{2}{k+3}[/tex]
[tex]\\ \rm\Rrightarrow k+3=6k[/tex]
[tex]\\ \rm\Rrightarrow 5k=3[/tex]
[tex]\\ \rm\Rrightarrow k=3/5[/tex]
