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}
$