Question

Determine a equação da reta que passa pelos pontos A= (3,2) B= (4,6)

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Answer 1

$\boxed{\begin{array}{l}\sf Seja~A(x_A,y_A)~e~B(x_B,y_B)~dois~pontos~quaisquer.\\\sf a~equac_{\!\!}\tilde ao~da~reta~que~passa~por~A~e~B~\acute e\\\begin{vmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{vmatrix}=0\end{array}}$

$\large\boxed{\begin{array}{l}\begin{vmatrix}\sf 3&\sf2&\sf1\\\sf4&\sf6&\sf1\\\sf x&\sf y&\sf1\end{vmatrix}=0\\\sf3\cdot(6-y)-2\cdot(4-x)+1\cdot(4y-6x)=0\\\sf 18-3y-8+2x+4y-6x=0\\\sf-4x+y+10=0\cdot(-1)\\\sf 4x-y-10=0\end{array}}$