Answer
$y=-\displaystyle \frac{11}{5}x+\frac{8}{5}$
Work Step by Step
$\left|\begin{array}{lll}
a_{1} & b_{1} & c_{1}\\
a_{2} & b_{2} & c_{2}\\
a_{3} & b_{3} & c_{3}
\end{array}\right|$ = see p.645...
$=a_{1}b_{2}c_{3}+b_{1}c_{2}a_{3}+c_{1}a_{2}b_{3}-a_{3}b_{2}c_{1}-b_{3}c_{2}a_{1}-c_{3}a_{2}b_{1}$
---------------------
Using the given formula with
$(x_{1},y_{1})=(3,-5)$
$(x_{2},y_{2})=(-2,6)$
$\left|\begin{array}{lll}
x & y & 1\\
3 & -5 & 1\\
-2 & 6 & 1
\end{array}\right|=0$
$-5x+(-2y)+18-10-6x-3y=0$
$-11x-5y+8=0$
Slope-inteercept is the form where this equation is solved for y:
$-5y=11x-8\qquad/\div(-5)$
$y=-\displaystyle \frac{11}{5}x+\frac{8}{5}$
