Precalculus, Chapter 1, 1.3, Section 1.3, Problem 44

Determine an equation of the line $L$.







Since the two lines are perpendicular, the product of their slopes must be $-1$. We use the given equation to find the slope. The line $y = -x$ has a slope $-1$. So, any line perpendicular to this line will have slope $1$. By using the point slope form to find the equation with point $(-1,1)$. We have,


$
\begin{equation}
\begin{aligned}

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


\end{aligned}
\end{equation}
$