Finite Mathematics, Chapter 1, Review Exercises, Section Review Exercises, Problem 16

Determine an equation in the form $y = mx + b$ (where possible) for the line
that goes through $(2,-3)$ and $(-3,4)$
Let $(x_1 , y_1) = (2, -3)$ and $(x_2 , y_2) = (-3, 4)$.

$
\begin{equation}
\begin{aligned}
y - ( - 3) &= \frac{4 - (-3)}{-3 - 2} (x - 2)\\
\\
y + 3 &= \frac{4 + 3}{- 3 - 2} ( x- 2 )\\
\\
y + 3 &= \frac{-7}{5} (x - 2)\\
\\
y + 3 &= \frac{-7}{5}x + \frac{14}{5}\\
\\
y &= \frac{-7}{5}x - \frac{1}{5}
\end{aligned}
\end{equation}
$