Answer:
1
Step-by-step explanation:
1) First, place the given equation in slope-intercept form ([tex]y = mx +b[/tex] format) to find its slope easier. Isolate the y:
[tex]2x + 2y = 28\\2y = -2x + 28\\y = -x+14[/tex]
So, the equation of the line in slope-intercept form is [tex]y = -x + 14[/tex]. When an equation is in slope-intercept form, the [tex]m[/tex], or the coefficient of the x-term, represents the slope. Thus, the slope for the given line would be -1.
2) Lines that are perpendicular have slopes that are opposite reciprocals of each other. We need to find the opposite reciprocal of -1, then.
To find the opposite reciprocal of a number, write the given number as a fraction first -- making -1 be written as [tex]-\frac{1}{1}[/tex] -- then switch the sign and flip the numerator and denominator. So, the opposite reciprocal of -1 is 1, and 1 is the slope of the perpendicular line.
