Final answer:
The slope of a line that is perpendicular to the line with the equation 2x+2y=28 is 1, calculated by taking the negative reciprocal of the original line's slope which is -1.
Step-by-step explanation:
To find the slope of a line perpendicular to the line given by the equation 2x+2y=28, we first need to find the slope of the original line. We start by rewriting the equation in the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. Let's solve for y:
2y = -2x + 28
y = -x + 14
The slope of the original line (m) is -1. The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the slope of the line perpendicular to the original line will be:
mperpendicular = -1 / (-1)
mperpendicular = 1
The slope of the line perpendicular to the original line with an equation 2x+2y=28 is 1.