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 $(x_1, y_1) = (5,9)$


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