Question

Determine m de modo que as retas: 2x-3y+4=0 e mx+4y=0 sejam:
a) Paralelas b) Perpendiculares

Answer 1

Retas paralelas possuem o mesmo coeficiente angular, por isso:

$2x-3y+4=0\\\\ 3y=2x+3\\\\ y=\frac{2x}{3}+\frac{4}{3}$

$mx+4y=0\\\\ -4y=mx\\\\ y=-\frac{mx}{4}$

Agora, basta igualar os termos que acompanham o x

$\frac{2}{3}=-\frac{m}{4}\\\\ \\\\ 2*4 = 3*-m\\\\ 8 = -3m\\\\ \boxed{m=-\frac{8}{3}}$

Retas perpendiculares

$m_r*m_s=-1\\\\ \frac{2}{3}*-\frac{m}{4}=-1\\\\ -\frac{2m}{12}=1\\\\ -2m=12\\\\ -m=\frac{12}{2}\\\\ \boxed{m=-6}$