Evaluate a Third-Order Determinant
-The Equation of a Line Passing $\left( \mathrm { x } _ { 1 } , \mathrm { y } _ { 1 } \right)$

Multiple Choice

Evaluate a Third-Order Determinant
-The equation of a line passing through two distinct points $\left( \mathrm { x } _ { 1 } , \mathrm { y } _ { 1 } \right)$ and $\left( \mathrm { x } _ { 2 } , \mathrm { y } _ { 2 } \right)$ is given by $\left| \begin{array} { l l l } x & y & 1 \\ x _ { 2 } & y _ { 2 } & 1 \\ x _ { 3 } & y _ { 3 } & 1 \end{array} \right| = 0$ . Use the determinant to write an equation for the line passing through $( 9 , - 5 )$ and $( - 8,3 )$ . Express the line's equation in standard form.

A) $- 8 x - 17 y - 13 = 0$
B) $- 5 x - 8 y + 27 = 0$
C) $8 x + 17 y - 13 = 0$
D) $3 x + 9 y + 40 = 0$