Choose the One Alternative That Best Completes the Statement or Answers

Multiple Choice

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

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