Determinants Are Used to Show That Three Points Lie on the Same

Multiple Choice

Determinants are used to show that three points lie on the same line (are collinear) . If
-The equation of a line passing through two distinct points (x1, y1) and (x2, y2) is given by $\left|\begin{array}{lll}x & y & 1 \\x_{2} & y 2 & 1 \\x_{3} & y_{3} & 1\end{array}\right|=0 . \text { Use the determinant to write an equation for the line passing through }(-6,9) \text { and }$
$( - 8,3 )$ . Express the line's equation in standard form.

A) $6 x - 2 y + 54 = 0$
B) $9 x - 8 y - 18 = 0$
C) $- 6 x + 2 y + 54 = 0$
D) $3 x - 6 y - 72 = 0$