Question

qual é soma do coeficiente angular com o coeficiente linear da reta que passa pelos pontos A(1,-1) e B(-2,-7)

Answer 1

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

$\Large\boxed{\begin{array}{l}\sf A(1,-1)~B(-2,-7)\\\sf m=\dfrac{y_B-y_A}{x_B-x_A}\\\\\sf m=\dfrac{-7-(-1)}{-2-1}=\dfrac{-7+1}{-3}=\dfrac{-6}{-3}=2\\\sf adotando~o~ponto~A(1,-1)~temos:\\\sf y=-1+2\cdot(x-1)\\\sf y=-1+2x-2\\\sf y=2x-3\\\sf m=2~~n=-3\\\sf m+n=2+(-3)\\\sf m+n=2-3\\\sf m+n=-1\end{array}}$