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}
$