Beginning Algebra With Applications, Chapter 5, Review Exercises, Section Review Exercises, Problem 6

Determine the slope of the line that contains the points whose coordinates are $(3,-4)$ and $(1,-4)$.

Let $(x_1, y_1) = (3,-4)$ and $(x_2,y_2) = (1,-4) $

Using the slope of the line formula


$
\begin{equation}
\begin{aligned}

m =& \frac{y_2 - y_1}{x_2 - x_1}
\\
\\
m =& \frac{-4-(-4)}{1-3}
\\
\\
m =& \frac{0}{-2}
\\\
\\
m =& 0

\end{aligned}
\end{equation}
$



Using Point Slope Form, where $m=0$ and $(x_1, y_1) = (3,-4)$


$
\begin{equation}
\begin{aligned}

y - y_2 =& m(x - x_1)
&&
\\
y-(-4) =& 0(x-3)
&& \text{Substitute $m = 0$ and $(x_1, y_1) = (3,-4)$}
\\
y+4 =& 0
&& \text{Apply Distributive Property}
\\
y =& -4
&& \text{Subtract } 4

\end{aligned}
\end{equation}
$