Melody08
Answered

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Sagot :

#1

[tex]\\ \rm\Rrightarrow 2y=x-4[/tex]

[tex]\\ \rm\Rrightarrow y=x/2-2[/tex]

  • m=1/2

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]

  • m=6

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]

  • m1=1/3k

[tex]\\ \rm\Rrightarrow y=(2/k+3)x-6/(k+3)[/tex]

  • m2=2/k+3

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]

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