Intermediate Algebra, Chapter 3, Test, Section Test, Problem 12

Determine an equation of the line "through $(-2,3)$ and $(6,-1)$", and write it in the following form:

a.) Slope-intercept form

Using the Slope Formula

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 3}{6 - (-2)} = - \frac{4}{8} = - \frac{1}{2}$

The slope is $\displaystyle - \frac{1}{2}$.

Using Point Slope Form


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
\\
y - 3 =& - \frac{1}{2} [x - (-2)]
&& \text{Substitute } x = -2, y = 3 \text{ and } m = - \frac{1}{2}
\\
\\
y - 3 =& - \frac{1}{2}x - 1
&& \text{Distributive Property}
\\
\\
y =& - \frac{1}{2}x + 2
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$



b.) Standard Form


$
\begin{equation}
\begin{aligned}

& y = - \frac{1}{2}x + 2
&& \text{Slope Intercept Form}
\\
\\
& \frac{1}{2}x + y = 2
&& \text{Standard Form}
\\
& \text{or}
&&
\\
& x + 2y = 4
&&

\end{aligned}
\end{equation}
$