Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 38

Determine the equation of the line through the points whose coordinates are $(-3,9)$ and $(1,1)$.

Using the Slope Formula with $(x_1, y_1) = (-3,9)$ and $(x_2, y_2) = (1,1)$

$\displaystyle m = \frac{1-9}{1-(-3)} = \frac{-8}{4} = -2$

The slope of the line is $-2$.

Using the point slope formula with $m = -2$ and $(x_1, y_1) = (-3,9)$


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$