Answer
$y=-\displaystyle \frac{1}{5}x+\frac{23}{5}$
Work Step by Step
$A=(x_{1},y_{1})=(3, \ 4)$
$B=(x_{2},y_{2})=(-2, \ 5)$
The increments in the coordinates are calculated as $\left\{\begin{array}{l}
\Delta x=x_{2}-x_{1}\\
\Delta y=y_{2}-y_{1}
\end{array}\right.$
$\left\{\begin{array}{l}
\Delta x=-2-3=-5\\
\Delta y=6-4=1
\end{array}\right.$
Neither of the increments is zero; so the line is neither vertical nor horizontal.
The slope of the line that passes through A and B, if the line is nonvertical, ($\Delta x\neq 0)$ is calculated as
$m=\displaystyle \frac{\Delta y}{\Delta x}=\frac{1}{5}==-\frac{1}{5}$,
The point-slope equation of a line containing the point $(x_{1},y_{1})$, with slope $m$
is$\quad y=y_{1}+m(x-x_{1})$
Given $(x_{1},y_{1})=(3,4)$ and $m=-\displaystyle \frac{1}{5}$
$y=4+(-\displaystyle \frac{1}{5})(x-3)$
$y=4-\displaystyle \frac{1}{5}x+\frac{3}{5}$
$y=-\displaystyle \frac{1}{5}x+\frac{20+3}{5}$
$y=-\displaystyle \frac{1}{5}x+\frac{23}{5}$
