Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 52

Determine the equation of the line through the points whose coordinates are $(14,-1)$ and $(-7,-7)$.

Using the Slope Formula with $(x_1, y_1) = (14,-1)$ and $(x_2, y_2) = (-7,-7)$

$\displaystyle m = \frac{-7-(-1)}{-7-14} = \frac{-6}{-21} = \frac{2}{7}$

The slope of the line is $\displaystyle \frac{2}{7}$.

Using the point slope formula with $\displaystyle m = \frac{2}{7}$ and $(x_1, y_1) = (14,-1)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
y-(-1) =& \frac{2}{7} (x-14)
&& \text{Substitute } m = \frac{2}{7}, (x_1, y_1) = (14,-1)
\\
y+1 =& \frac{2}{7}x - 4
&& \text{Apply Distributive Property}
\\
y =& \frac{2}{7}x - 5
&& \text{Write the slope-intercept form}

\end{aligned}
\end{equation}
$