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}$