Answer
$y=\displaystyle \frac{1}{3}x+\frac{10}{3}$
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...
$=a_{1}b_{2}c_{3}+b_{1}c_{2}a_{3}+c_{1}a_{2}b_{3}-a_{3}b_{2}c_{1}-b_{3}c_{2}a_{1}-c_{3}a_{2}b_{1}$
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Using the given formula with
$(x_{1},y_{1})=(-1,3)$
$(x_{2},y_{2})=(2,4)$
$\left|\begin{array}{lll}
x & y & 1\\
-1 & 3 & 1\\
2 & 4 & 1
\end{array}\right|=0$
$3x+2y+(-4)-6-4x-(-y)=0$
$-x+3y-10=0$
For slope-intercept form, this equation is solved for y:
$3y=x+10\qquad/\div(3)$
$y=\displaystyle \frac{1}{3}x+\frac{10}{3}$