Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 34

Determine the equation of the line parallel to the line $x + y = 2$ and containing the point $(1,-3)$. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.


Since two lines are parallel, their slopes must be equal. Using the equation $x + y = 2$ to find the slope. We write the equation in slope intercept form, we have


$
\begin{equation}
\begin{aligned}

& x + y = 2
\\
& y = -x + 2

\end{aligned}
\end{equation}
$


The slope is $-1$. Now $(1,-3)$ is a point on the line. Using point slope form,


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
&&
\\
y - (-3) =& -1(x-1)
&& \text{Substitute $m = -1, x = 1$ and $y = -3$}
\\
y + 3 =& -x + 1
&& \text{Simplify}
\\
y =& -x - 2
&& \text{Slope Intercept Form}
\\
x + y =& -2
&& \text{General Form}

\end{aligned}
\end{equation}
$