Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 30

Using the point slope formula, find the equation of the line that passes through the point whose coordinates are $(3,-2)$ and has slope of $\displaystyle \frac{1}{6}$


$
\begin{equation}
\begin{aligned}

(x_1, y_1) =& (3,-2)
&& \text{Let $(x_1, y_1)$ be the given point}
\\
m =& \frac{1}{6}
&& \text{$m$ is the given slope}
\\
y - y_1 =& m(x- x_1)
&& \text{Point slope formula}
\\
y -(-2) =& \frac{1}{6} (x-3)
&& \text{Substitute $3$ for $x$, $-2$ for $y$ and } \frac{1}{6} \text{ for $m$}
\\
y +2=& \frac{1}{6}x - \frac{1}{2}
&& \text{Rewrite the equation in the form } y = mx+b
\\
y =& \frac{1}{6}x - \frac{5}{2}
&& \text{Add } -2

\end{aligned}
\end{equation}
$