Solve the Problem $\left( x _ { 1 } , y _ { 1 } \right)$

Multiple Choice

Solve the problem.
-The equation of the line passing through the distinct points $\left( x _ { 1 } , y _ { 1 } \right)$ and (x $\left. 2 , y _ { 2 } \right)$ is given by $\left| \begin{array} { l l l } x _ { 1 } & y _ { 1 } & 1 \\ x _ { 2 } & y _ { 2 } & 1 \end{array} \right| = 0 .$ Find the equation of the line passing through the points $( 3,5 )$ and $( - 1,4 )$ .

A) x + 4y + 17 = 0
B) -x + 4y - 17 = 0
C) x + 7y + 17 = 0
D) x - 4y + 17 = 0