Question

Sobre Paralelismo: as retas r:2x-5y+3=0 e s:(p+1)x-y+11=0 são paralelas. Determine p.

Answer 1

Se as retas são PARALELAS possuem o MESMO COEFICIENTE ANGULAR.

1) CALCULAR O COEFICIENTE ANGULAR DA RETA R:

$\left\{\begin{array}{ccc}2x-5y+3=0\\\\\boxed{m= -\frac{a}{b} = -\frac{2}{-5} = \frac{2}{5}}\end{array}\right$

2) CALCULAR O COEFICIENTE ANGULAR DA RETA S:

$\left\{\begin{array}{ccc}(p+1)x-y+11=0\\\\\boxed{m = \frac{-(p+1)}{-1} = p+1}\end{array}\right$

3) IGUALAR OS COEFICIENTES ANGULARES:

$Resolu\c{c}\~ao \to \left\{\begin{array}{ccc}m_r = m_s\\\\\frac{2}{5} = p+1\\\\5*(p+1) = 2\\\\5p+5=2\\\\5p = 2-5\\\\5p = -3\\\\\boxed{\boxed{p=-\frac{3}{5}}}\end{array}\right$

Espero ter ajudado. =^.^=