Question

Defina a equação reduzida da reta que se intercepta nos pontos A(-1 , 5) e B(2 , 1)

Answer 1

Olá !

Resolução :

$\left(\begin{array}{ccc}-1&5&1\\2&1&1\\X&Y&1\end{array}\right\left)\begin{array}{ccc}-1&5&\\2&1&\\X&Y&\end{array}\right$

$\textbf{CALCULANDO~~A~~EQUACAO~~GERAL}$

$\mathsf{-1 + 5X + 2Y - X + Y - 10 = 0 } \\\\\\\\\ \mathsf{5X - X + 2Y + Y - 10 - 1 = 0 } \\\\\\\\\ \mathsf{4X + 3Y - 11 = 0 }$

$\textbf{CALCULANDO~~A~~EQUACAO~~REDUZIDA}$

$\texttt{COEFICIENTE ~~ANGULAR}$

$\mathsf{m =\dfrac{-a}{b}} \\\\\\\\\ \mathsf{m =\dfrac{-4}{3}} \\\\\\\\\ \mathsf{ m= -\dfrac{4}{3}}$

$\texttt{COEFICIENTE ~~LINEAR}$

$\mathsf{ n =\dfrac{-c}{b}} \\\\\\\\\ \mathsf{ n=\dfrac{-(-11)}{3}} \\\\\\\\\ \mathsf{ n =\dfrac{11}{3}}$

$\textbf{SABEMOS ~~QUE~~TODA~~EQUACAO~~REDUZIDA~~DA~~RETA}$

$\textbf{E~~DADA~~POR~~:}$
$\textbf{Y = mx + n}$

$\textbf{LOGO~~:}$

$\mathsf{Y =-\dfrac{4}{3}~~+~~\dfrac{11}{3}}$

$\mathsf{RESPOSTA ~~:}$

$\mathsf{Y =-\dfrac{4}{3}x~~+~~\dfrac{11}{3}}$