Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 56

Determine the equation of the line through the points whose coordinates are $(-3,6)$ and $(4,-8)$.

Using the Slope Formula with $(x_1, y_1) = (-3,6)$ and $(x_2, y_2) = (4,-8)$

$\displaystyle m = \frac{-8-6}{4-(-3)} = \frac{-14}{7} = -2
$

The slope of the line is $\displaystyle -2$.

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


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$