Question

Questão 34- Qual é a equação reduzida da reta t que passa pelos pontos R(0, 4) e S(1, 1)? * 1 ponto a) y=4x-3 b) y=-4x+3 c) y=-3x+4 d) y=3x-4​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Coeficiente~angular}\\\sf Dados~dois~pontos~A(x_A,y_A)~B(x_B,y_B)~\\\sf o~coeficiente~angular~m~\acute e~dada~por\\\sf m=\dfrac{y_B-y_A}{x_B-x_A}\\\underline{\rm Equac_{\!\!,}\tilde ao~da~reta~na~forma}\\\underline{\rm ponto~coeficiente-angular}\\\sf y=y_0+m(x-x_0)\\\sf sendo~x_0~e~y_0~coordenadas\\\sf do~ponto~escolhido.\\\underline{\rm equac_{\!\!,}\tilde ao~da~reduzida~da~reta}\\\sf y=mx+n\end{array}}$

$\large\boxed{\begin{array}{l}\sf R(0,4)~S(1,1)\\\sf m=\dfrac{y_S-y_R}{x_S-x_R}\\\\\sf y=\dfrac{1-4}{1-0}\\\\\sf m=\dfrac{-3}{1}\\\\\sf m=-3\\\sf adotando~o~ponto~R(0,4):\\\sf y=4+(-3)\cdot(x-0)\\\sf y=4-3x\longrightarrow equac_{\!\!,}\tilde ao~procurada\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~b}}}} \end{array}}$