Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 42

Determine the equation of the line through the points whose coordinates are $(-6,-13)$ and $(6,-1)$.

Using the Slope Formula with $(x_1, y_1) = (-6,-13)$ and $(x_2, y_2) = (6,-1)$

$\displaystyle m = \frac{-1-(-13)}{6-(-6)} = \frac{12}{12} = 1$

The slope of the line is $1$.

Using the point slope formula with $\displaystyle m = 1$ and $(x_1, y_1) = (-6,-13)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
y-(-13) =& 1[x - (-6)]
&& \text{Substitute } m = 1, (x_1, y_1) = (-6,-13)
\\
y+13 =& x+6
&& \text{Apply Distributive Property}
\\
y =& x-7
&& \text{Write the slope-intercept form}

\end{aligned}
\end{equation}
$