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}$