Question

Determine a equação geral da reta que passa pelos ponto:
(2-1)e(-3,2):

Answer 1

$\large\boxed{\begin{array}{l}\rm Dados\,dois\,pontos\,A( x_A.y_A)\,e\,B(x_B,y_B)\\\rm o\,coeficiente\,angular\,que\,passa\\\rm por\,A\,e\,B\,\acute e\\\rm m=\dfrac{y_B-y_A}{x_B-x_A}.\\\underline{\sf Equac_{\!\!,}\tilde ao\,da\,reta\,que\,passa\,por\,P(x_0,y_0)}\\\underline{\sf e\,tem\,coeficiente\,angular\,m}\\\rm y=y_0+m(x-x_0)\end{array}}$

$\large\boxed{\begin{array}{l}\rm A(-2,1)~~B(-3,2)\\\rm m=\dfrac{2-1}{-3-[-2]}=\dfrac{1}{-3+2}=\dfrac{1}{-1}=-1\\\\\rm adotando\,o\,ponto\,A(1,-2)\,temos\\\rm y=1+[-1](x-[-2])\\\rm y=1-1(x+2)\\\rm y=1-x-2\\\rm y=-x-1\\\rm escrevendo\,na\,forma\,geral:\\\rm r:x+y+1=0\end{array}}$