Question

SPAECE). Dois pontos pertencentes à reta r são (– 2, 3) e (1,6). Qual é a equação dessa reta? *


A) y = – 3x – 3

B) y = – 2x + 3

C) y = x + 5

D) y = x + 6

​

Answer 1

$A\subset r,\ B\subset r,\ r\in\mathbb{R}^2.$

$A(x_A,y_A)=A(-2,3)$

$B(x_B,y_B)=B(1,6)$

$\mathrm{A}\ \mathbf{equa\c{c}\tilde{a}o\ geral\ da\ reta}\ \mathrm{pode\ ser\ obtida\ da\ seguinte}\ \text{maneira:}$

$\left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x&y&1\end{array}\right| =0$

$\text{Logo:}$

$\left|\begin{array}{ccc}-2&3&1\\1&6&1\\x&y&1\end{array}\right|=0$

$\Longrightarrow -12+3x+y-6x+2y-3=0$

$\Longrightarrow -3x+3y-15=0\Longrightarrow -x+y-5=0$

$\Longrightarrow r:x-y+5=0\Longleftarrow \mathbf{Equa\c{c}\tilde{a}o\ geral\ da\ reta.}$

$\Longrightarrow \boxed{y=x+5}\Longleftarrow \mathbf{Equa\c{c}\tilde{a}o\ reduzida\ da\ reta.}$

$\mathrm{Letra\ C.}$