Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 22

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


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$