Answer:
[tex]y=-x[/tex]
Step-by-step explanation:
The slope-intercept form of a line can be written as [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope, [tex]b[/tex] is the y-intercept, and [tex](x,y)[/tex] are the coordinates of any point that this line passes through.
Perpendicular lines have negative-reciprocal slopes. Therefore a line perpendicular to [tex]y=x+2[/tex] will have a slope of [tex]-\frac{1}{1}=-1[/tex].
Now that we have a slope and coordinates of a point that the line passes through, we can solve for the y-intercept and the equation of the line:
[tex]-2=-1(2)+b, \\b=0[/tex]
Thus, the equation of this line is [tex]\fbox{$y=-x$}[/tex].
