Precalculus, Chapter 1, 1.3, Section 1.3, Problem 42

Determine an equation of the line $L$.







Since the two lines are parallel, the slope of the line that we need equals the slope of the line $y = -x$. The equation is in slope intercept form where in the slope is $-1$. So the other also has slope $-1$ and contains the point $(1,2)$. By using Point Slope Form to find the equation


$
\begin{equation}
\begin{aligned}

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


\end{aligned}
\end{equation}
$