We have the following line equation:
y = -x+7
Remember that the canonical form of the line equation is
y = mx + b
where m is the slope of the line. In our case we have
y = -x+ 7
that is
y = (-1) x + 7
then the slope of the above line is (-1) , therefore the slope of the line perpendicular to this line is the negative reciprocal of -1 , that is - 1/(-1), that is 1.