The Determinant $\left| \begin{array} { l l l } x & y & 1 \\x _ { 2 } & y _ { 2 } & 1 \\x _ { 3 } & y _ { 3 } & 1\end{array} \right| = 0$

Multiple Choice

The determinant $\left| \begin{array} { l l l } x & y & 1 \\x _ { 2 } & y _ { 2 } & 1 \\x _ { 3 } & y _ { 3 } & 1\end{array} \right| = 0$ is the equation of a line through the points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right) .$ Use this formula to find the equation of the line passing through the points $( - 1,8 )$ and $( 4 , - 7 )$

A) $5 x - y = - 3$
B) $3 x + y = - 5$
C) $- 3 x + y = - 5$
D) $3 x - y = - 5$
E) $- 3 x - y = - 5$