Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 26

Using the point slope formula, find the equation of the line that passes through the point whose coordinates are $(3,-1)$ and has slope of $\displaystyle \frac{2}{3}$


$\begin{equation} \begin{aligned} (x_1, y_1) =& (3,-1) && \text{Let $(x_1, y_1)$ be the given point} \\ m =& \frac{2}{3} && \text{$m$ is the given slope} \\ y - y_1 =& m(x- x_1) && \text{Point slope formula} \\ y - (-1) =& \frac{2}{3} (x-3) && \text{Substitute $3$ for $x$, $-1$ for $y$ and } \frac{2}{3} \text{ for $m$} \\ y + 1 =& \frac{2}{3} x - 2 && \text{Rewrite the equation in the form } y = mx+b \\ y =& \frac{2}{3}x - 3 && \text{Add $-1$} \end{aligned} \end{equation}$