Question

Assinale a equação geral da reta que passa pelo ponto P( 3,2) e é paralela à reta s: 12x -4y +1 = 0 

a) 3x - y +7 = 0

b) x - y +7 = 0

c) -3x + y +7 = 0

d) - y +8 = 0 ​

Answer 1

$\Large\boxed{\begin{array}{l}\sf r:ax+by+c=0\implies m_r=-\dfrac{a}{b}\\\\\sf s: mx+ny+k=0\implies m_s=-\dfrac{m}{n}\\\\\sf r\parallel s\iff m_r=m_s\end{array}}$

$\Large\boxed{\begin{array}{l}\sf s: 12x-4y+1=0\implies m_s=-\dfrac{12}{-4}=3\\\sf r\parallel s\iff m_r=m_s=3\\\sf y=y_0+m\cdot(x-x_0)\\\sf y=2+3\cdot(x-3)\\\sf y=2+3x-9\\\sf y=3x-7\\\sf -3x+y+7=0\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~c}}}}\end{array}}$