Final answer:
The slope of a line perpendicular to the line with equation 2x + 2y = 24 is 1, as the slope of the given line is -1 and the slope of a perpendicular line is the negative reciprocal of the original slope.
Step-by-step explanation:
To find the slope of a line perpendicular to the given line with equation 2x + 2y = 24, we first need to rewrite this equation in slope-intercept form, which is y = mx + b. Here, 'm' represents the slope and 'b' represents the y-intercept.
First, let's isolate y in the given equation:
• 2y = -2x + 24
• Divide by 2: y = -1 * x + 12
Now, we have y = -x + 12, which indicates that the slope of the given line is -1. The slope of a line that is perpendicular to another line is the negative reciprocal of the slope of the first line. Therefore, the slope of the perpendicular line is:
Slope of perpendicular line = -1 * (-1) = 1
The slope of the line perpendicular to 2x + 2y = 24 is 1.