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 $(x_2 , y_2) = (-3, 4)$.

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