Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 40

Determine the equation of the line through the points whose coordinates are $(-6,12)$ and $(-4,9)$.

Using the Slope Formula with $(x_1, y_1) = (-6,12)$ and $(x_2, y_2) = (-4,9)$

$\displaystyle m = \frac{9-12}{-4-(-6)} = \frac{-3}{2}$

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

Using the point slope formula with $\displaystyle m = \frac{-3}{2}$ and $(x_1, y_1) = (-6,12)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
y-12 =& \frac{-3}{2} [x- (-6)]
&& \text{Substitute } m = \frac{-3}{2}, (x_1, y_1) = (-6,12)
\\
y - 12 =& \frac{-3}{2}x - 9
&& \text{Apply Distributive Property}
\\
y =& \frac{-3}{2}x+ 3
&& \text{Write the slope-intercept form}

\end{aligned}
\end{equation}
$