Answer
$\color{blue}{y=x+2}$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is:
$y=mx+b$
where $m$=slope and $b$ = y-intercept.
(2) Perpendicular lines have slopes whose product is $-1$.
Line $L$ is perpendicular to the line $y=-x$, whose slope is $-1$.
Since $L$ is perpendicular to this line, then $L$ has a slope of $1$ (since $-1 \cdot 1=-1$)
Thus, the tentative equation of the line is $y=x+b$.
To find the value of $b$, substitute the x and y values of the point $(-1, 1)$ into the tentative equation above to obtain:
$y=x+b
\\1=-1 + b
\\1+1=b
\\2=b$
Therefore, the equation of line $L$ is $\color{blue}{y=x+2}$.
