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

$\\ \rm\Rrightarrow \dfrac{1}{3k}=\dfrac{2}{k+3}$

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

$\\ \rm\Rrightarrow 5k=3$

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