Question

os pontos (3, -2) (a, 5) e (b, 100) pertencem a uma reta paralela ao eixo y. determine a e b.

Answer 1

$\text{F\'ormula para achar a equac\~ao da reta:}\\\\\\\\\dfrac{x}{Px}+\dfrac{y}{Py}=1\\\\\\\\\dfrac{x}{3}+\dfrac{y}{-2}=1\\\\\\\\\text{Tirando o mmc com o 6:}$


$\dfrac{2x}{6}+\dfrac{-3y}{6}=\dfrac{6}{6}\\\\\\\\2x-3y=6\\\\\\\\2x-3y-6=0\\\\\\\\\text{Pronto, encontramos a equac\~ao! Agora basta substituir valores para encontrar a e b, veja:}$


$a:\\\\2x-3y-6=0\\\\\\\\2x-3\cdot 5-6=0\\\\\\\\2x-15-6=0\\\\\\\\2x-21=0\\\\\\\\2x=21\\\\\\\\x=\dfrac{21}{2}\\\\\\\\\boxed{x=10,5}$


$b:\\\\2x-3y-6=0\\\\\\\\2x-3\cdot 100-6=0\\\\\\\\2x-300-6=0\\\\\\\\2x-306=0\\\\\\\\2x=306\\\\\\\\x=\dfrac{306}{2}\\\\\\\\\boxed{x=153}\\\\\\\\\text{D\'uvidas? Comente.}$