Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 48

Determine the equation of the line through the points whose coordinates are $(-6,19)$ and $(2,7)$.

Using the Slope Formula with $(x_1, y_1) = (-6,19)$ and $(x_2, y_2) = (2,7)$

$\displaystyle m = \frac{7-19}{2-(-6)} = \frac{-12}{8} = \frac{-3}{2}$

The slope of the line is $\displaystyle \frac{-3}{2}$.

Using the point slope formula with $\displaystyle m = \frac{-3}{2}$ and $(x_1, y_1) = (-6,19)$


$\begin{equation} \begin{aligned} y - y_1 =& m(x - x_1) && \\ y - 19 =& \frac{-3}{2} [x- (-6)] && \text{Substitute } m = \frac{-3}{2}, (x_1, y_1) = (-6,19) \\ y-19 =& \frac{-3}{2}x - 9 && \text{Apply Distributive Property} \\ y =& \frac{-3}{2}x + 10 && \text{Write the slope-intercept form} \end{aligned} \end{equation}$