Intermediate Algebra, Chapter 3, 3.3, Section 3.3, Problem 60

Determine an equation of the line passing through the points $(-2,2)$ and $(4,2)$.

(a) Write the equation in standard form.

Using the Slope Formula,

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2-2}{4-(-2)} = \frac{0}{6} = 0$

Using Point Slope Form, where $m = \displaystyle 0$ and $(x_1,y_1) = (-2,2)$



$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
y - 2 =& 0 [x - (-2)]
&& \text{Substitute } x = -2, y = 2 \text{ and } m = 0
\\
y - 2 =& 0
&& \text{Distributive Property}
\\
y =& 2
&& \text{Standard Form}

\end{aligned}
\end{equation}
$



(b) Write the equation in slope-intercept form.

The equation $y = 2$ is also the slope intercept form.