Question

MEE AJUUDEEMM

A equação da reta que passa pelo ponto P(3,-1) e é paralela à reta de equação x − 4y + 2 = 0

é:
$A) 3x - y - 2 = 0\\B) X - 7y - 4 = 0\\C) X - 3y - 2 = 0\\D) X - 4y - 7 = 0\\E) 3x - y = 0$

Answer 1

$\large\boxed{\begin{array}{l}\rm A~equac_{\!\!,}\tilde ao~da~reta~que~passa~pelo~ponto~P(3,-1)\\\rm e~\acute e~paralela~\grave a~reta~de~equac_{\!\!,}\tilde ao~x-4y+2=0~\acute e:\\\tt A)~\rm 3x-y-2=0\\\tt B)~\rm x-7y-4=0\\\tt C)~\rm x-3y-2=0\\\tt D)~\rm x-4y-7=0\\\tt E)~\rm 3x-y=0\end{array}}$

$\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf uma~reta~\acute e~paralela~a~outra\\\sf quando~o~coeficiente~angular~\acute e~o~mesmo.\\\sf x-4y+2=0\\\sf 4y=x+2\\\sf y=\dfrac{1}{4}x+\dfrac{2}{4}\\\sf assim~o~coeficiente~angular~\acute e~m=\dfrac{1}{4}\\\sf usando~a~equac_{\!\!,}\tilde ao~ponto-coeficiente~angular~temos:\\\sf y=y_0+m(x-x_0)\\\sf y=-1+\dfrac{1}{4}(x-3)\\\sf y=-1+\dfrac{1}{4}x-\dfrac{3}{4}\\\underline{\rm multiplicando~a~igualdade~por~4~temos:}\\\sf 4y=-4+x-3\end{array}}$

$\large\boxed{\begin{array}{l}\sf4y=x-7\\\underline{\rm escrevendo~a~equac_{\!\!,}\tilde ao~na~forma~geral~temos:}\\\sf x-4y-7=0\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~D}}}}\end{array}}$