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

Multiple Choice

The equation $$\left| \begin{array} { l l l } x & y & 1 \\x _ { 1 } & y _ { 1 } & 1 \\x _ { 2 } & y _ { 2 } & 1\end{array} \right| = 0$$ = 0 represents an equation of the line passing through distinct points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$ a. Use the determinant equation to write an equation of the line passing through the given points.
b. Write the equation of the line in slope-intercept form.
- $( - 2,6 )$ and $( - 3,2 )$

A) a. $\left| \begin{array} { r r r } x & y & 1 \\ - 2 & 6 & 1 \\ - 3 & 2 & 1 \end{array} \right| = 0 ;$ b. $y = - 8 x - 10$
B) $\mathbf { a } . \left| \begin{array} { c c c } x & y & 1 \\ - 2 & - 3 & 1 \\ 6 & 2 & 1 \end{array} \right| = 0 ;$ b. $y = 4 x + 14$
C) $\mathbf { a } . \left| \begin{array} { c c c } x & y & 1 \\ - 2 & - 3 & 1 \\ 6 & 2 & 1 \end{array} \right| = 0 ;$ b. $y = - 8 x - 10$
D) a. $\left| \begin{array} { r r r } x & y & 1 \\ - 2 & 6 & 1 \\ - 3 & 2 & 1 \end{array} \right| = 0 ;$ b. $y = 4 x + 14$