Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 44

Determine the equation of the line through the points whose coordinates are $(-3,-4)$ and $(5,-4)$.

Using the Slope Formula with $(x_1, y_1) = (-3,-4)$ and $(x_2, y_2) = (5,-4)$

$\displaystyle m = \frac{-4-(-4)}{5-(-3)} = \frac{0}{8} = 0$

The slope of the line is .

Using the point slope formula with $\displaystyle m = 0$ and $(x_1, y_1) = (-3,-4)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
y-(-4) =& 0 [x-(-3)]
&& \text{Substitute } m = 0, (x_1, y_1) = (-3,-4)
\\
y +4 =& 0
&& \text{Simplify}
\\
y =& -4
&& \text{Write the slope-intercept form}

\end{aligned}
\end{equation}
$