Question

Escreva a equação geral da reta que passa pelos pontos.
a) (2; 1) e (4; -3)
b) (6; -1) e (3; 2)
c) (10; 0) e (1; -1)

Answer 1

m = (y2 – y1) / (x2 – x1)

m = –3 – 6 / 2 – (–1)

m = –9 / 3

m = –3  

y – y1 = m (x – x1).

y – 6 = –3 (x + 1)

y – 6 = –3x – 3

y – 6 + 3x + 3 = 0

y + 3x – 3 = 0

3x + y – 3 = 0

x * (–6) * 1 = 6x

y * 1 * 2 = 2y

1 * (–1) * (–3) = 3    

1* 6 * 2 = 12

x * 1 * (–3) = –3x

y * (–1) * 1 = –y  

s: 6x + 2y + 3 – (12 – 3x – y) = 0

s: 6x + 2y + 3 – 12 + 3x + y = 0

s: 9x + 3y – 9 = 0  

s: 3x + y – 3 = 0

$s= \left[\begin{array}{ccc}x&y&1\\-1&6&1\\2&-3&1\end{array}\right] \\\\s=\left[\begin{array}{ccc}x&y&1\\-1&6&1\\2&-3&1\end{array}\right] \left[\begin{array}{ccc}x&y&\\-1&6&\\2&-3&\end{array}\right]$