Question

Para que valor de k,as retas r : 2 x - 3 y + 9 = 0 e s : kx - 12y + 7 =0 são retas paralelas : *

A) 8
B) 7
C) 6
D) 5
E) 4​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm D~\!\!efinic_{\!\!,}\tilde ao~de~paralelismo}\\\sf r: ax+by+c=0\implies m_r=-\dfrac{a}{b}\\\\\sf s: bx+dy+f=0\implies m_s=-\dfrac{b}{d}\\\sf r\parallel s\iff m_r=m_s\end{array}}$

$\Large\boxed{\begin{array}{l}\sf r: 2x-3y+9=0\implies m_r=-\dfrac{2}{-3}=\dfrac{2}{3}\\\\\sf s: kx-12y+7=0\implies m_s=-\dfrac{k}{-12}=\dfrac{k}{12}\\\sf r\parallel s\iff m_r=m_s\\\sf\dfrac{2}{3}=\dfrac{k}{12}\\\\\sf 3k=24\\\\\sf k=\dfrac{24}{3}\\\\\sf k=8\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~A}}}}\end{array}}$