Beginning Algebra With Applications, Chapter 5, Review Exercises, Section Review Exercises, Problem 26

Determine the equation of the line through the points whose coordinates are $(4,14)$ and $(-8,-1)$.

We let $(x_1, y_1) = (4,14)$ and $(x_2, y_2) = (-8,-1)$

Using Slope of the line Formula,


$
\begin{equation}
\begin{aligned}

m =& \frac{y_2 - y_1}{x_2 - x_1}
\\
\\
m =& \frac{-1-14}{-8-14}
\\
\\
m =& \frac{-15}{-12}
\\
\\
m =& \frac{5}{4}


\end{aligned}
\end{equation}
$


Using the point slope form, where $\displaystyle m = \frac{5}{4}$ and $(x_1, y_1) = (4,14)$



$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
\\
y - 14 =& \frac{5}{4}(x-4)
&& \text{Substitute } m = \frac{5}{4} \text{ and } (x_1, y_1) = (4,19)
\\
\\
y-14 =& \frac{5}{4}x - 5
&& \text{Apply Distributive Property}
\\
\\
y =& \frac{5}{4}x + 9
&& \text{Add } 14

\end{aligned}
\end{equation}
$