Explanation:
the slope of a line is always the factor of x, when the line is in the form
y = ...
so,
3x + 3y = 18
3y = -3x + 18
y = -x + 6
the slope is -1 = -1/1
as the slope is the ratio of y coordinate change / x coordinate change.
a perpendicular slope switches x and y upside-down and flips the sign.
so, in our case the perpendicular slope is
1/1 = 1