Question

A equação da reta que passa pelos pontos (2, -3) e (8, 1) é:

a) 2x – 3y – 13 = 0

b) -2x – 3y + 13 = 0

c) 3x – 2y + 13 = 0

d) 2x – 3y + 13 = 0

e) 2x + 3y – 13 = 0

Answer 1

$\left|\begin{array}{ccc}x&y&1\\2&-3&1\\8&1&1\end{array}\right|=0\\ \\ -3x+8y+2+24-2y-x=0\\ \\ -4x+6y+26=0\\ \\ \boxed{2x-3y-13=0} \ \ LETRA \ A$

Answer 2

$f(x)=ax+b$

$f(2)=-3$

$2a+b=-3~~(i)$

$f(8)=1$

$8a+b=1~~(ii)$

Subtraindo $(ii)$ de $(i)$:

$(8a+b)-(2a+b)=1-(-3)$

$6a=4$

$a=\dfrac{2}{3}$


$2a+b=-3$

$\dfrac{4}{3}+b=-3$

$4+3b=-9$

$3b=-13$

$b=\dfrac{-13}{3}$

$y=\dfrac{2}{3}x-\dfrac{13}{3}$

Multiplicando os dois membros por $3$:

$3y=2x-13$

$2x-3y-13=0$

Letra A