Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 54

Determine the equation of the line through the points whose coordinates are $(5,9)$ and $(-5,3)$.

Using the Slope Formula with $(x_1, y_1) = (5,9)$ and $(x_2, y_2) = (-5,3)$

$\displaystyle m = \frac{3-9}{-5-5} = \frac{-6}{-10} = \frac{3}{5}
$

The slope of the line is $\displaystyle \frac{3}{5}$.

Using the point slope formula with $\displaystyle m = \frac{3}{5}$ and $(x_1, y_1) = (5,9)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
y - 9 =& \frac{3}{5} (x-5)
&& \text{Substitute } m = \frac{3}{5}, (x_1, y_1) = (5,9)
\\
y-9 =& \frac{3}{5}x - 3
&& \text{Apply Distributive Property}
\\
y =& \frac{3}{5}x + 6
&& \text{Write the slope-intercept form}

\end{aligned}
\end{equation}
$