First put the equation in slope intercept form ( y = mx+b)
2x+2y = 24
Divide each side by 2
x+y = 12
Subtract x from each side
y = -x+12
The slope of this equation is -1
Perpendicular lines have slopes that multiply to -1
m * -1 = -1
Divide by -1
m = 1
The slope of a line perpendicular to this line is 1