Question

Determine a equação geral da reta que possa que passa pelos pontos a (1,2) b (5,7)​

Answer 1

Utilizando o método do determinante, temos:

$\left|\begin{array}{ccc}x_a&y_a&1\\x_b&y_b&1\\x&y&1\end{array}\right|~=~0\\\\\\\\\left|\begin{array}{ccc}1&2&1\\5&7&1\\x&y&1\end{array}\right|~=~0\\\\\\(~1.7.1~+~5.y.1~+~x.2.1~)~-~(~1.7.x~+~1.y.1~+~1.2.5~)~=~0\\\\\\(~7~+~5y~+~2x~)~-~(~7x~+~y~+~10~)~=~0\\\\\\7~+~5y~+~2x~-~7x~-~y~-~10~=~0\\\\\\-5x~+~4y~-~3~=~0\\\\\\\boxed{5x~-~4y~+~3~=~0}$