Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 32

Determine the equation of the line containing the points $(3,-4)$ and $(2,1)$. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.

Using the Formula for slope,

$\displaystyle m = \frac{1-(-4)}{2-3} = \frac{5}{-1} = -5$

Then by using point slope form to find the equation,


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
&&
\\
y - (-4) =& -5(x-3)
&& \text{Substitute $m = -5, x = 3$ and $y = -4$}
\\
y + 4 =& -5x + 15
&& \text{Simplify}
\\
y =& -5x + 11
&& \text{Slope Intercept Form}
\\
5x + y =& 11
&& \text{General Form}

\end{aligned}
\end{equation}
$