Question

sabendo que a reta s passa pelo ponto A (-2,8) e possui inclinação= 120°, escreva a equação reduzida​

Answer 1

A equação reduzida da reta é dada por:

$y-y_o~=~m\,.\,(x-x_o)\\\\\\Onde~"m",~o~coeficiente~angular~\acute{e}~dado~por:\\\\\\m~=~tg\,\left(^{inclinacao}_{~\,da~reta}\right)$

Sendo assim, temos:

$m~=~tg(120^\circ)\\\\\\m~=~-tg(180^\circ-120^\circ)\\\\\\m~=~-tg(60^\circ)\\\\\\\boxed{m~=~-\sqrt{3}}\\\\\\\\y-y_o~=~m\,.\,(x-x_o)\\\\\\y-8~=~-\sqrt{3}\,.\,(x-(-2))\\\\\\y-8~=~-\sqrt{3}\,.\,(x+2)\\\\\\\boxed{y~=~-\sqrt{3}\,.\,x~-~2\sqrt{3}~+~8}\\\\\\ou\\\\\\\boxed{y~=~-\sqrt{3}\,.\,x+\left(8-2\sqrt{3}\,\right)}$