Find the slope of a line perpendicular to the line whose equation is 2, x, plus, 2, y, equals, 242x+2y=24. Fully simplify your answer.
To find the slope of a line perpendicular to the given line, we first need to rewrite the equation in slope-intercept form, y = mx + b.
2x + 2y = 24
Divide all terms by 2:
x + y = 12
y = -x + 12
Now we can see that the slope of the given line is -1, since the coefficient of x is -1.
The slope of a line perpendicular to this line will be the negative reciprocal of -1:
m_perpendicular = -1/m = -1/(-1) = 1
Therefore, the slope of a line perpendicular to the given line is 1.